Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
85801	Integrate Using u-Substitution	integral of (9r^2)/( square root of 1-r^3) with respect to r	$\int \frac{9 r^{2}}{\sqrt{1 - r^{3}}} d r$
85802	Integrate Using u-Substitution	integral from pi/4 to pi/3 of cos(x)sin(x) with respect to x	$\int_{\frac{π}{4}}^{\frac{π}{3}} \cos (x) \sin (x) d x$
85803	Integrate Using u-Substitution	integral of (e^x)/(e^x+1) with respect to x	$\int \frac{e^{x}}{e^{x} + 1} d x$
85804	Integrate Using u-Substitution	integral of e^(tan(x))sec(x)^2 with respect to x	$\int e^{\tan (x)} \sec^{2} (x) d x$
85805	Integrate Using u-Substitution	integral from pi/6 to pi/4 of tan(u) with respect to u	$\int_{\frac{π}{6}}^{\frac{π}{4}} \tan (u) d u$
85806	Integrate Using u-Substitution	integral from -6 to 0 of \|x^3+27\| with respect to x	$\int_{- 6}^{0} \| x^{3} + 27 \| d x$
85807	Integrate Using u-Substitution	integral of (x^3)/(x^4-5) with respect to x , u=x^4-5	$\int \frac{x^{3}}{x^{4} - 5} d x$ , $u = x^{4} - 5$
85808	Integrate Using u-Substitution	integral of x^5(x^3+1)^(1/2) with respect to x	$\int x^{5} {(x^{3} + 1)}^{\frac{1}{2}} d x$
85809	Integrate Using u-Substitution	integral of csc(2x) with respect to x	$\int \csc (2 x) d x$
85810	Integrate Using u-Substitution	integral of ( natural log of x)/(x^2) with respect to x	$\int \frac{\ln (x)}{x^{2}} d x$
85811	Integrate Using u-Substitution	integral of (cos(1/x))/(x^2) with respect to x	$\int \frac{\cos (\frac{1}{x})}{x^{2}} d x$
85812	Integrate Using u-Substitution	integral of 2/( square root of x) with respect to x	$\int \frac{2}{\sqrt{x}} d x$
85813	Integrate Using u-Substitution	integral of x^(1/3)(x^(4/3)+5)^8 with respect to x	$\int x^{\frac{1}{3}} {(x^{\frac{4}{3}} + 5)}^{8} d x$
85814	Integrate Using u-Substitution	integral of (12x)/( cube root of 3-x^2) with respect to x	$\int \frac{12 x}{\sqrt[3]{3 - x^{2}}} d x$
85815	Integrate Using u-Substitution	integral of 3x^5 square root of x^3+1 with respect to x	$\int 3 x^{5} \sqrt{x^{3} + 1} d x$
85816	Integrate Using u-Substitution	integral of sec(1-x)tan(1-x) with respect to x	$\int \sec (1 - x) \tan (1 - x) d x$
85817	Integrate Using u-Substitution	integral of (8x)/((4x^2-1)^4) with respect to x	$\int \frac{8 x}{{(4 x^{2} - 1)}^{4}} d x$
85818	Integrate Using u-Substitution	integral of ( natural log of x+4)/(x+4) with respect to x	$\int \frac{\ln (x + 4)}{x + 4} d x$
85819	Integrate Using u-Substitution	integral from 0 to 4 of square root of 2x+1 with respect to x	$\int_{0}^{4} \sqrt{2 x + 1} d x$
85820	Integrate Using u-Substitution	integral of (2x+5)(x^2+5x)^7 with respect to x	$\int (2 x + 5) {(x^{2} + 5 x)}^{7} d x$
85821	Integrate Using u-Substitution	integral from -pi/4 to 0 of tan(x)sec(x)^2 with respect to x	$\int_{- \frac{π}{4}}^{0} \tan (x) \sec^{2} (x) d x$
85822	Integrate Using u-Substitution	integral of (18x+4)(9x^2+4x)^5 with respect to x	$\int (18 x + 4) {(9 x^{2} + 4 x)}^{5} d x$
85823	Integrate Using u-Substitution	integral of sin(x)^5cos(x)^2 with respect to x	$\int \sin^{5} (x) \cos^{2} (x) d x$
85824	Integrate Using u-Substitution	integral of (4x)/(5(6x^2-7)^(2/3)) with respect to x	$\int \frac{4 x}{5 {(6 x^{2} - 7)}^{\frac{2}{3}}} d x$
85825	Integrate Using u-Substitution	integral of square root of cos(6x)sin(6x) with respect to x	$\int \sqrt{\cos (6 x)} \sin (6 x) d x$
85826	Integrate Using u-Substitution	integral of (h^3(2h^4-2)^5)/4 with respect to h	$\int \frac{h^{3} {(2 h^{4} - 2)}^{5}}{4} d h$
85827	Integrate Using u-Substitution	integral of (cos( square root of t))/( square root of t) with respect to t	$\int \frac{\cos (\sqrt{t})}{\sqrt{t}} d t$
85828	Integrate Using u-Substitution	integral from 1 to 2 of e^(1-x) with respect to x	$\int_{1}^{2} e^{1 - x} d x$
85829	Integrate Using u-Substitution	integral from 0 to pi/4 of tan(x)sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} \tan (x) \sec^{2} (x) d x$
85830	Integrate Using u-Substitution	integral of (2x+1)(x^2+x) with respect to x	$\int (2 x + 1) (x^{2} + x) d x$
85831	Integrate Using u-Substitution	integral of (3x^2)/( square root of x^3+1) with respect to x	$\int \frac{3 x^{2}}{\sqrt{x^{3} + 1}} d x$
85832	Integrate Using u-Substitution	integral of (2x)/(x^2+1) with respect to x	$\int \frac{2 x}{x^{2} + 1} d x$
85833	Integrate Using u-Substitution	integral from 0 to 2 of x square root of 4-x^2 with respect to x	$\int_{0}^{2} x \sqrt{4 - x^{2}} d x$
85834	Integrate Using u-Substitution	integral of natural log of ( square root of 1-x)/(x+1) with respect to x	$\int \ln (\frac{\sqrt{1 - x}}{x + 1}) d x$
85835	Integrate Using u-Substitution	integral of 20/((5x-9)^2) with respect to x	$\int \frac{20}{{(5 x - 9)}^{2}} d x$
85836	Integrate Using u-Substitution	integral of -sin(x)cos(x)^7 with respect to x	$\int - \sin (x) \cos^{7} (x) d x$
85837	Integrate Using u-Substitution	integral from 6/pi to 2/(3pi) of (cos(1/x))/(x^2) with respect to x	$\int_{\frac{6}{π}}^{\frac{2}{3 π}} \frac{\cos (\frac{1}{x})}{x^{2}} d x$
85838	Integrate Using u-Substitution	integral of (x^3)/( square root of 4+x^2) with respect to x	$\int \frac{x^{3}}{\sqrt{4 + x^{2}}} d x$
85839	Integrate Using u-Substitution	integral from 0 to pi/6 of cos(3x)sin(sin(3x)) with respect to x	$\int_{0}^{\frac{π}{6}} \cos (3 x) \sin (\sin (3 x)) d x$
85840	Integrate Using u-Substitution	integral of e^(cos(pix))sin(pix) with respect to x	$\int e^{\cos (π x)} \sin (π x) d x$
85841	Integrate Using u-Substitution	integral of (3x^2)/((8-3x^3)^5) with respect to x	$\int \frac{3 x^{2}}{{(8 - 3 x^{3})}^{5}} d x$
85842	Integrate Using u-Substitution	integral from 0 to 1 of (e^x)/(e^x+1) with respect to x	$\int_{0}^{1} \frac{e^{x}}{e^{x} + 1} d x$
85843	Integrate Using u-Substitution	integral from -1 to 2 of 2^x with respect to x	$\int_{- 1}^{2} 2^{x} d x$
85844	Integrate Using u-Substitution	integral of 9x^2 square root of 1-x^3 with respect to x	$\int 9 x^{2} \sqrt{1 - x^{3}} d x$
85845	Integrate Using u-Substitution	integral of 12x^2(2x^3+3)^7 with respect to x	$\int 12 x^{2} {(2 x^{3} + 3)}^{7} d x$
85846	Integrate Using u-Substitution	integral of 1/( square root of x square root of 1-x) with respect to x	$\int \frac{1}{\sqrt{x} \sqrt{1 - x}} d x$
85847	Integrate Using u-Substitution	integral from 1 to 2 of (x-4)/(x^2) with respect to x	$\int_{1}^{2} \frac{x - 4}{x^{2}} d x$
85848	Integrate Using u-Substitution	( integral of x^2 natural log of x^2+1 with respect to x)	$(\int x^{2} \ln (x^{2} + 1) d x)$
85849	Integrate Using u-Substitution	integral of x/( fourth root of x+2) with respect to x	$\int \frac{x}{\sqrt[4]{x + 2}} d x$
85850	Integrate Using u-Substitution	integral of 8(y^4+4y^2+1)^2(y^3+2y) with respect to y	$\int 8 {(y^{4} + 4 y^{2} + 1)}^{2} (y^{3} + 2 y) d y$
85851	Integrate Using u-Substitution	integral of x/((x^2+1)^2) with respect to x	$\int \frac{x}{{(x^{2} + 1)}^{2}} d x$
85852	Integrate Using u-Substitution	integral of (21x^2)/(4(x^3+5)^(5/4)) with respect to x	$\int \frac{21 x^{2}}{4 {(x^{3} + 5)}^{\frac{5}{4}}} d x$
85853	Integrate Using u-Substitution	integral from 0 to (pi^2)/4 of (sin( square root of x))/( square root of x) with respect to x	$\int_{0}^{\frac{π^{2}}{4}} \frac{\sin (\sqrt{x})}{\sqrt{x}} d x$
85854	Integrate Using u-Substitution	integral of (x^3)/((x^2+4)^(3/2)) with respect to x	$\int \frac{x^{3}}{{(x^{2} + 4)}^{\frac{3}{2}}} d x$
85855	Integrate Using u-Substitution	integral of 1/(1+4x^2) with respect to x	$\int \frac{1}{1 + 4 x^{2}} d x$
85856	Integrate Using u-Substitution	integral of (x+ square root of x) with respect to x	$\int (x + \sqrt{x}) d x$
85857	Integrate Using u-Substitution	integral of (20x^3+8)/(5x^4+8x+3) with respect to x	$\int \frac{20 x^{3} + 8}{5 x^{4} + 8 x + 3} d x$
85858	Integrate Using u-Substitution	integral from pi/4 to (3pi)/4 of csc(x) with respect to x	$\int_{\frac{π}{4}}^{\frac{3 π}{4}} \csc (x) d x$
85859	Integrate Using u-Substitution	integral of 3/((3-2x)^2) with respect to x	$\int \frac{3}{{(3 - 2 x)}^{2}} d x$
85860	Integrate Using u-Substitution	integral of ( square root of 1+x^2)/x with respect to x	$\int \frac{\sqrt{1 + x^{2}}}{x} d x$
85861	Integrate Using u-Substitution	integral of 10/( square root of 2x+3) with respect to x	$\int \frac{10}{\sqrt{2 x + 3}} d x$
85862	Integrate Using u-Substitution	integral of 1/( square root of 1+x^2) with respect to x	$\int \frac{1}{\sqrt{1 + x^{2}}} d x$
85863	Integrate Using u-Substitution	integral of sin(-5x^4-x-6)(-20x^3-1) with respect to x	$\int \sin (- 5 x^{4} - x - 6) (- 20 x^{3} - 1) d x$
85864	Integrate Using u-Substitution	integral of (2x^2)/( square root of 1-4x^3) with respect to x	$\int \frac{2 x^{2}}{\sqrt{1 - 4 x^{3}}} d x$
85865	Integrate Using u-Substitution	integral of (e^(3x))/(1+e^(3x)) with respect to x	$\int \frac{e^{3 x}}{1 + e^{3 x}} d x$
85866	Integrate Using u-Substitution	integral of x^2sin(x^3) with respect to x	$\int x^{2} \sin (x^{3}) d x$
85867	Integrate Using u-Substitution	integral of (2x+7)(x^2+7x+3)^(4/5) with respect to x	$\int (2 x + 7) {(x^{2} + 7 x + 3)}^{\frac{4}{5}} d x$
85868	Integrate Using u-Substitution	integral of 4x^3sin(x^4) with respect to x	$\int 4 x^{3} \sin (x^{4}) d x$
85869	Integrate Using u-Substitution	integral of x square root of 1+x^2 with respect to x	$\int x \sqrt{1 + x^{2}} d x$
85870	Integrate Using u-Substitution	integral of square root of x^5-8*5x^4 with respect to x	$\int \sqrt{x^{5} - 8} \cdot 5 x^{4} d x$
85871	Integrate Using u-Substitution	integral of (18x^2+3)(6x^3+3x)^6 with respect to x	$\int (18 x^{2} + 3) {(6 x^{3} + 3 x)}^{6} d x$
85872	Integrate Using u-Substitution	integral of (1+2x)^4*3x with respect to x	$\int {(1 + 2 x)}^{4} \cdot 3 x d x$
85873	Integrate Using u-Substitution	integral of x^3 cube root of x^2+4 with respect to x	$\int x^{3} \sqrt[3]{x^{2} + 4} d x$
85874	Integrate Using u-Substitution	integral of x/( square root of 2x-1) with respect to x	$\int \frac{x}{\sqrt{2 x - 1}} d x$
85875	Integrate Using u-Substitution	integral of cos(x)*5^(sin(x)) with respect to x	$\int \cos (x) \cdot 5^{\sin (x)} d x$
85876	Integrate Using u-Substitution	integral from 0 to 1 of x/( square root of x+1) with respect to x	$\int_{0}^{1} \frac{x}{\sqrt{x + 1}} d x$
85877	Integrate Using u-Substitution	integral of (3^(2x))/(1+3^(2x)) with respect to x	$\int \frac{3^{2 x}}{1 + 3^{2 x}} d x$
85878	Integrate Using u-Substitution	integral of (9x^2)/((5-2x^3)^4) with respect to x	$\int \frac{9 x^{2}}{{(5 - 2 x^{3})}^{4}} d x$
85879	Integrate Using u-Substitution	integral from 0 to 1 of 2x(x^2+1)^2 with respect to x	$\int_{0}^{1} 2 x {(x^{2} + 1)}^{2} d x$
85880	Integrate Using u-Substitution	integral of 1/(4x+9) with respect to x	$\int \frac{1}{4 x + 9} d x$
85881	Integrate Using u-Substitution	integral of (3x^4+2)^4(12x^3) with respect to x	$\int {(3 x^{4} + 2)}^{4} (12 x^{3}) d x$
85882	Integrate Using u-Substitution	integral of 1/(x square root of 9x^2-1) with respect to x	$\int \frac{1}{x \sqrt{9 x^{2} - 1}} d x$
85883	Integrate Using u-Substitution	integral of sin(x)*e^(cos(x)) with respect to x	$\int \sin (x) \cdot e^{\cos (x)} d x$
85884	Integrate Using u-Substitution	integral from 2 to 4 of 1/(5-3x) with respect to x	$\int_{2}^{4} \frac{1}{5 - 3 x} d x$
85885	Integrate Using u-Substitution	integral of 1/( cube root of 9x-1) with respect to x	$\int \frac{1}{\sqrt[3]{9 x - 1}} d x$
85886	Integrate Using u-Substitution	integral of x^3(1-x^2)^(3/2) with respect to x	$\int x^{3} {(1 - x^{2})}^{\frac{3}{2}} d x$
85887	Integrate Using u-Substitution	integral of (e^(tan(x)))/(cos(x)^2) with respect to x	$\int \frac{e^{\tan (x)}}{\cos^{2} (x)} d x$
85888	Integrate Using u-Substitution	integral of 5 square root of 5x-1dx with respect to x	$\int 5 \sqrt{5 x - 1 d x} d x$
85889	Integrate Using u-Substitution	integral of xsin(x^2)^2 with respect to x	$\int x \sin^{2} (x^{2}) d x$
85890	Integrate Using u-Substitution	integral from 0 to pi/2 of cos(x)sin(sin(x)) with respect to x	$\int_{0}^{\frac{π}{2}} \cos (x) \sin (\sin (x)) d x$
85891	Integrate Using u-Substitution	integral of 1/(x square root of natural log of x) with respect to x	$\int \frac{1}{x \sqrt{\ln (x)}} d x$
85892	Integrate Using u-Substitution	integral of arctan(x) with respect to x	$\int \arctan (x) d x$
85893	Integrate Using u-Substitution	integral of 1/(x square root of 4- natural log of x^2) with respect to x	$\int \frac{1}{x \sqrt{4 - \ln^{2} (x)}} d x$
85894	Integrate Using u-Substitution	integral of (csc( square root of x)cot( square root of x))/( square root of x) with respect to x	$\int \frac{\csc (\sqrt{x}) \cot (\sqrt{x})}{\sqrt{x}} d x$
85895	Integrate Using u-Substitution	integral of 4(6x+1)^5 with respect to x	$\int 4 {(6 x + 1)}^{5} d x$
85896	Integrate Using u-Substitution	integral from 0 to 2 of e^(2x) with respect to x	$\int_{0}^{2} e^{2 x} d x$
85897	Integrate Using u-Substitution	integral of (x^3+1)^2 with respect to x	$\int {(x^{3} + 1)}^{2} d x$
85898	Integrate Using u-Substitution	integral of (8x-12)(4x^2-12x)^4 with respect to x	$\int (8 x - 12) {(4 x^{2} - 12 x)}^{4} d x$
85899	Integrate Using u-Substitution	integral of ((e^x+1)^2)/(e^x) with respect to x	$\int \frac{{(e^{x} + 1)}^{2}}{e^{x}} d x$
85900	Integrate Using u-Substitution	integral of x^6 with respect to x	$\int x^{6} d x$