Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
27601	Evaluate the Integral	integral of 3(q-4)^2 with respect to q	$\int 3 {(q - 4)}^{2} d q$
27602	Evaluate the Integral	integral from 3 to 4 of 24-6x with respect to x	$\int_{3}^{4} 24 - 6 x d x$
27603	Evaluate the Integral	integral from 3 to 4 of 0.2e^(-0.2A)+6/A with respect to A	$\int_{3}^{4} 0.2 e^{- 0.2 A} + \frac{6}{A} d A$
27604	Evaluate the Integral	integral from -3 to 3 of - square root of 9-x^2 with respect to x	$\int_{- 3}^{3} - \sqrt{9 - x^{2}} d x$
27605	Evaluate the Integral	integral from 3 to 4 of e^(3.5x) with respect to x	$\int_{3}^{4} e^{3.5 x} d x$
27606	Evaluate the Integral	integral from 3 to 4 of (x^3-2x^2-4)/(x^3-2x^2) with respect to x	$\int_{3}^{4} \frac{x^{3} - 2 x^{2} - 4}{x^{3} - 2 x^{2}} d x$
27607	Evaluate the Integral	integral from -3 to 4 of 3e^x-4 with respect to x	$\int_{- 3}^{4} 3 e^{x} - 4 d x$
27608	Evaluate the Integral	integral from 3 to 6 of 9/x with respect to x	$\int_{3}^{6} \frac{9}{x} d x$
27609	Evaluate the Integral	integral from 3 to 5 of 3x with respect to x	$\int_{3}^{5} 3 x d x$
27610	Evaluate the Integral	integral from 3 to 5 of 2x+7 with respect to x	$\int_{3}^{5} 2 x + 7 d x$
27611	Evaluate the Integral	integral from 3 to 5 of 1/(1+t) with respect to tdt	$\int_{3}^{5} \frac{1}{1 + t} d t d t$
27612	Evaluate the Integral	integral from 0 to (3pi)/16 of (cos(4x))/4+(sin(4x))/4 with respect to x	$\int_{0}^{\frac{3 π}{16}} \frac{\cos (4 x)}{4} + \frac{\sin (4 x)}{4} d x$
27613	Evaluate the Integral	integral from 0 to (13pi)/6 of 8sin(x)+4cos(x) with respect to x	$\int_{0}^{\frac{13 π}{6}} 8 \sin (x) + 4 \cos (x) d x$
27614	Evaluate the Integral	integral of z/(2z^2+8) with respect to z	$\int \frac{z}{2 z^{2} + 8} d z$
27615	Evaluate the Integral	integral from 0 to 1/2 of 1/( square root of 1-r^2) with respect to r	$\int_{0}^{\frac{1}{2}} \frac{1}{\sqrt{1 - r^{2}}} d r$
27616	Evaluate the Integral	integral from 0 to 1/2 of 4cos(pix) with respect to x	$\int_{0}^{\frac{1}{2}} 4 \cos (π x) d x$
27617	Evaluate the Integral	integral from 0 to 1/2 of xcos(pix) with respect to x	$\int_{0}^{\frac{1}{2}} x \cos (π x) d x$
27618	Evaluate the Integral	integral from 0 to (3pi)/4 of cos(x) with respect to x	$\int_{0}^{\frac{3 π}{4}} \cos (x) d x$
27619	Evaluate the Integral	integral from 0 to pi/4 of 8sec(x)^2 with respect to x	$\int_{0}^{\frac{π}{4}} 8 \sec^{2} (x) d x$
27620	Evaluate the Integral	integral from 0 to 0.786 of xsin(x)^2 with respect to x	$\int_{0}^{0.786} x \sin^{2} (x) d x$
27621	Evaluate the Integral	integral of z^2( natural log of (z)^2) with respect to z	$\int z^{2} (\ln ({(z)}^{2})) d z$
27622	Evaluate the Integral	integral from 0 to (3 square root of 3)/2 of (x^3)/( square root of 4x^2+9) with respect to x	$\int_{0}^{\frac{3 \sqrt{3}}{2}} \frac{x^{3}}{\sqrt{4 x^{2} + 9}} d x$
27623	Evaluate the Integral	integral from 0 to ( square root of 2)/2 of (x^2)/( square root of 1-x^2) with respect to x	$\int_{0}^{\frac{\sqrt{2}}{2}} \frac{x^{2}}{\sqrt{1 - x^{2}}} d x$
27624	Evaluate the Integral	integral of ye^(2y) with respect to y	$\int y e^{2 y} d y$
27625	Evaluate the Integral	integral of y^3 with respect to x	$\int y^{3} d x$
27626	Evaluate the Integral	integral of ye^(xy) with respect to x	$\int y e^{x y} d x$
27627	Evaluate the Integral	integral of ye^(-y) with respect to y	$\int y e^{- y} d y$
27628	Evaluate the Integral	integral of y^3(2y^2-3) with respect to y	$\int y^{3} (2 y^{2} - 3) d y$
27629	Evaluate the Integral	integral of (xsec(x)tan(x)+3x^2+ square root of x)/x with respect to x	$\int \frac{x \sec (x) \tan (x) + 3 x^{2} + \sqrt{x}}{x} d x$
27630	Simplify	e^( natural log of x+ natural log of 6)	$e^{\ln (x) + \ln (6)}$
27631	Evaluate the Integral	integral of y^(5/2) with respect to y	$\int y^{\frac{5}{2}} d y$
27632	Evaluate the Integral	integral of xe^x-ye^x with respect to x	$\int x e^{x} - y e^{x} d x$
27633	Evaluate the Integral	integral of (-xy)/(a^2-x^2) with respect to x	$\int \frac{- x y}{a^{2} - x^{2}} d x$
27634	Evaluate the Integral	integral of xe^(ax) with respect to x	$\int x e^{a x} d x$
27635	Evaluate the Integral	integral of xy^2 with respect to y	$\int x y^{2} d y$
27636	Evaluate the Integral	integral of y/((y+4)(2y-1)) with respect to y	$\int \frac{y}{(y + 4) (2 y - 1)} d y$
27637	Evaluate the Integral	integral of y/(e^y) with respect to y	$\int \frac{y}{e^{y}} d y$
27638	Evaluate the Integral	integral of y/( square root of 5-y) with respect to y	$\int \frac{y}{\sqrt{5 - y}} d y$
27639	Evaluate the Integral	integral of xe^(-2x^2) with respect to x	$\int x e^{- 2 x^{2}} d x$
27640	Evaluate the Integral	integral of xe^(11x) with respect to x	$\int x e^{11 x} d x$
27641	Evaluate the Integral	integral of xe^(x/6) with respect to x	$\int x e^{\frac{x}{6}} d x$
27642	Evaluate the Integral	integral of xe^(-6x) with respect to x	$\int x e^{- 6 x} d x$
27643	Evaluate the Integral	integral of xe^(7x^2) with respect to x	$\int x e^{7 x^{2}} d x$
27644	Evaluate the Integral	integral of xe^(5x^2) with respect to x	$\int x e^{5 x^{2}} d x$
27645	Evaluate the Integral	integral of xe^(7x) with respect to x	$\int x e^{7 x} d x$
27646	Evaluate the Integral	integral of xe^(-7x) with respect to x	$\int x e^{- 7 x} d x$
27647	Evaluate the Integral	integral from 0 to pi/12 of sin(6x)^3 with respect to x	$\int_{0}^{\frac{π}{12}} \sin^{3} (6 x) d x$
27648	Evaluate the Integral	integral from 0 to pi/12 of 18tan(3x) with respect to x	$\int_{0}^{\frac{π}{12}} 18 \tan (3 x) d x$
27649	Evaluate the Integral	integral from 0 to pi/2 of (2sin(2t))/(5-cos(2t)) with respect to t	$\int_{0}^{\frac{π}{2}} \frac{2 \sin (2 t)}{5 - \cos (2 t)} d t$
27650	Evaluate the Integral	integral from 0 to pi/2 of (2sin(2t))/(6-cos(2t)) with respect to t	$\int_{0}^{\frac{π}{2}} \frac{2 \sin (2 t)}{6 - \cos (2 t)} d t$
27651	Evaluate the Integral	integral from 0 to pi/2 of sin(x)+cos(x) with respect to x	$\int_{0}^{\frac{π}{2}} \sin (x) + \cos (x) d x$
27652	Evaluate the Integral	integral from 0 to pi/2 of e^(sin(7pix))cos(7pix) with respect to x	$\int_{0}^{\frac{π}{2}} e^{\sin (7 π x)} \cos (7 π x) d x$
27653	Evaluate the Integral	integral from 0 to pi/2 of (cos(x))/( square root of 1+sin(x)) with respect to x	$\int_{0}^{\frac{π}{2}} \frac{\cos (x)}{\sqrt{1 + \sin (x)}} d x$
27654	Evaluate the Integral	integral from 0 to pi/2 of sin(2x)^2 with respect to x	$\int_{0}^{\frac{π}{2}} \sin^{2} (2 x) d x$
27655	Evaluate the Integral	integral from 0 to pi/18 of cos(9x)sin(sin(9x)) with respect to x	$\int_{0}^{\frac{π}{18}} \cos (9 x) \sin (\sin (9 x)) d x$
27656	Evaluate the Integral	integral from 0 to pi/12 of cos(6x)sin(sin(6x)) with respect to x	$\int_{0}^{\frac{π}{12}} \cos (6 x) \sin (\sin (6 x)) d x$
27657	Evaluate the Integral	integral from 0 to pi/2 of 2tan(x) with respect to x	$\int_{0}^{\frac{π}{2}} 2 \tan (x) d x$
27658	Evaluate the Integral	integral from 0 to pi/2 of 6sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} 6 \sin (x) d x$
27659	Evaluate the Integral	integral from 0 to pi/2 of 3sin(x)^2cos(x)^2 with respect to x	$\int_{0}^{\frac{π}{2}} 3 \sin^{2} (x) \cos^{2} (x) d x$
27660	Evaluate the Integral	integral from 0 to pi/2 of cos(1/3x) with respect to x	$\int_{0}^{\frac{π}{2}} \cos (\frac{1}{3} x) d x$
27661	Evaluate the Integral	integral from 0 to pi/2 of 5sin(x)^(3/2)cos(x) with respect to x	$\int_{0}^{\frac{π}{2}} 5 {\sin (x)}^{\frac{3}{2}} \cos (x) d x$
27662	Evaluate the Integral	integral from 0 to pi/2 of cos(2x) with respect to x	$\int_{0}^{\frac{π}{2}} \cos (2 x) d x$
27663	Evaluate the Integral	integral from 0 to pi/2 of 2sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} 2 \sin (x) d x$
27664	Evaluate the Integral	integral from 0 to pi/2 of e^x-sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} e^{x} - \sin (x) d x$
27665	Evaluate the Integral	integral from 0 to pi/3 of e^(sin(x))cos(x) with respect to x	$\int_{0}^{\frac{π}{3}} e^{\sin (x)} \cos (x) d x$
27666	Evaluate the Integral	integral from 0 to pi/2 of x with respect to x	$\int_{0}^{\frac{π}{2}} x d x$
27667	Evaluate the Integral	integral from 0 to pi/3 of cos(x)^2 with respect to x	$\int_{0}^{\frac{π}{3}} \cos^{2} (x) d x$
27668	Evaluate the Integral	integral from 0 to pi/3 of 5tan(x)^5sec(x)^4 with respect to x	$\int_{0}^{\frac{π}{3}} 5 \tan^{5} (x) \sec^{4} (x) d x$
27669	Evaluate the Integral	integral from 0 to pi/3 of cos(2x) with respect to x	$\int_{0}^{\frac{π}{3}} \cos (2 x) d x$
27670	Evaluate the Integral	integral from 0 to pi/2 of sin(x)-cos(x) with respect to x	$\int_{0}^{\frac{π}{2}} \sin (x) - \cos (x) d x$
27671	Evaluate the Integral	integral from 0 to pi/2 of sin(x)+cos(x)sin(x) with respect to x	$\int_{0}^{\frac{π}{2}} \sin (x) + \cos (x) \sin (x) d x$
27672	Evaluate the Integral	integral from -2 to 2 of 8-2x^2 with respect to x	$\int_{- 2}^{2} 8 - 2 x^{2} d x$
27673	Evaluate the Integral	integral of x^y with respect to x	$\int x^{y} d x$
27674	Evaluate the Integral	integral of x^ne^x with respect to x	$\int x^{n} e^{x} d x$
27675	Evaluate the Integral	integral of x^8e^(x^9-6) with respect to x	$\int x^{8} e^{x^{9} - 6} d x$
27676	Evaluate the Integral	integral of x^5 square root of 3x^6+4 with respect to x	$\int x^{5} \sqrt{3 x^{6} + 4} d x$
27677	Evaluate the Integral	integral of x^5 natural log of 3x with respect to x	$\int x^{5} \ln (3 x) d x$
27678	Evaluate the Integral	integral of x^-6 natural log of x with respect to x	$\int x^{- 6} \ln (x) d x$
27679	Evaluate the Integral	integral of x^5sec(x^6)^2 with respect to x	$\int x^{5} \sec^{2} (x^{6}) d x$
27680	Evaluate the Integral	integral of x^4sec(2x^5) with respect to x	$\int x^{4} \sec (2 x^{5}) d x$
27681	Evaluate the Integral	integral of x^5(x^6-6)^4 with respect to x	$\int x^{5} {(x^{6} - 6)}^{4} d x$
27682	Evaluate the Integral	integral of (x+1)/(x^3+x^2-6x) with respect to x	$\int \frac{x + 1}{x^{3} + x^{2} - 6 x} d x$
27683	Evaluate the Integral	integral of (x+2)/( square root of 4-x^2) with respect to x	$\int \frac{x + 2}{\sqrt{4 - x^{2}}} d x$
27684	Evaluate the Integral	integral of (x-15)/( square root of x) with respect to x	$\int \frac{x - 15}{\sqrt{x}} d x$
27685	Evaluate the Integral	integral of (x-2)/x with respect to x	$\int \frac{x - 2}{x} d x$
27686	Evaluate the Integral	integral of (x-8)/(x^2-7x+10) with respect to x	$\int \frac{x - 8}{x^{2} - 7 x + 10} d x$
27687	Evaluate the Integral	integral of (x-9)/((x+5)(x-2)) with respect to x	$\int \frac{x - 9}{(x + 5) (x - 2)} d x$
27688	Evaluate the Integral	integral of (x-5)/( square root of x-6) with respect to x	$\int \frac{x - 5}{\sqrt{x - 6}} d x$
27689	Evaluate the Integral	integral of (x-6)/( square root of x) with respect to x	$\int \frac{x - 6}{\sqrt{x}} d x$
27690	Evaluate the Integral	integral of x^3+1/( square root of x) with respect to x	$\int x^{3} + \frac{1}{\sqrt{x}} d x$
27691	Evaluate the Integral	integral of x^3sin(2x^4) with respect to x	$\int x^{3} \sin (2 x^{4}) d x$
27692	Evaluate the Integral	integral of x^3sin(2x) with respect to x	$\int x^{3} \sin (2 x) d x$
27693	Evaluate the Integral	integral of x^33sin(x^34) with respect to x	$\int x^{33} \sin (x^{34}) d x$
27694	Evaluate the Integral	integral of x^4(x^3+8x^2+7) with respect to x	$\int x^{4} (x^{3} + 8 x^{2} + 7) d x$
27695	Evaluate	natural log of 1/15	$\ln (\frac{1}{15})$
27696	Evaluate the Integral	integral of x^3cos(x^4+6) square root of sin(x^4+6) with respect to x	$\int x^{3} \cos (x^{4} + 6) \sqrt{\sin (x^{4} + 6)} d x$
27697	Evaluate the Integral	integral of x^3+sin(22x)+((x+1)^3)/4 with respect to x	$\int x^{3} + \sin (22 x) + \frac{{(x + 1)}^{3}}{4} d x$
27698	Evaluate the Integral	integral of x^3 natural log of 6x with respect to x	$\int x^{3} \ln (6 x) d x$
27699	Evaluate the Integral	integral of x^4cos(2x) with respect to x	$\int x^{4} \cos (2 x) d x$
27700	Evaluate the Integral	integral of x^4 natural log of 4x with respect to x	$\int x^{4} \ln (4 x) d x$