Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
86001	Integrate Using u-Substitution	integral of (6x^2)/((4x^3-9)^3) with respect to x	$\int \frac{6 x^{2}}{{(4 x^{3} - 9)}^{3}} d x$
86002	Integrate Using u-Substitution	integral of (x^2-1)/( square root of 2x-1) with respect to x	$\int \frac{x^{2} - 1}{\sqrt{2 x - 1}} d x$
86003	Integrate Using u-Substitution	integral of (x+1)/(x^2+2x) with respect to x	$\int \frac{x + 1}{x^{2} + 2 x} d x$
86004	Integrate Using u-Substitution	integral of (5y-10)/(y^2-4y+11) with respect to y	$\int \frac{5 y - 10}{y^{2} - 4 y + 11} d y$
86005	Integrate Using u-Substitution	integral of (x^2)/( square root of 1-x^6) with respect to x	$\int \frac{x^{2}}{\sqrt{1 - x^{6}}} d x$
86006	Integrate Using u-Substitution	integral of ( natural log of square root of x)/x with respect to x	$\int \frac{\ln (\sqrt{x})}{x} d x$
86007	Integrate Using u-Substitution	integral of (4-x)^3 with respect to x	$\int {(4 - x)}^{3} d x$
86008	Integrate Using u-Substitution	integral of x^2 square root of 1+x^3 with respect to x	$\int x^{2} \sqrt{1 + x^{3}} d x$
86009	Integrate Using u-Substitution	integral from 0 to 8 of 1/( square root of 1+x) with respect to x	$\int_{0}^{8} \frac{1}{\sqrt{1 + x}} d x$
86010	Integrate Using u-Substitution	integral of x cube root of 3-2x with respect to x	$\int x \sqrt[3]{3 - 2 x} d x$
86011	Integrate Using u-Substitution	integral of (x+3)(x-1)^5 with respect to x	$\int (x + 3) {(x - 1)}^{5} d x$
86012	Integrate Using u-Substitution	integral from 0 to 3 of (x+1)^(1/2) with respect to x	$\int_{0}^{3} {(x + 1)}^{\frac{1}{2}} d x$
86013	Integrate Using u-Substitution	integral of (( square root of x+2)^2)/(5 square root of x) with respect to x	$\int \frac{{(\sqrt{x} + 2)}^{2}}{5 \sqrt{x}} d x$
86014	Integrate Using u-Substitution	integral from 0 to 1 of (x^3+x)(x^4+2x^2+9)^(1/2) with respect to x	$\int_{0}^{1} (x^{3} + x) {(x^{4} + 2 x^{2} + 9)}^{\frac{1}{2}} d x$
86015	Integrate Using u-Substitution	integral of 3x^2 with respect to x	$\int 3 x^{2} d x$
86016	Integrate Using u-Substitution	integral of 1/(1+16x^2) with respect to x	$\int \frac{1}{1 + 16 x^{2}} d x$
86017	Integrate Using u-Substitution	integral of (5x^2+1)^2(10x) with respect to x	$\int {(5 x^{2} + 1)}^{2} (10 x) d x$
86018	Integrate Using u-Substitution	integral of ((3x^2-2x+1)/x) with respect to x	$\int (\frac{3 x^{2} - 2 x + 1}{x}) d x$
86019	Integrate Using u-Substitution	integral from 0 to pi of sin(x) with respect to x	$\int_{0}^{π} \sin (x) d x$
86020	Integrate Using u-Substitution	integral of x/( square root of 1+x) with respect to x	$\int \frac{x}{\sqrt{1 + x}} d x$
86021	Integrate Using u-Substitution	integral of (6x)/( square root of 7-3x^2) with respect to x	$\int \frac{6 x}{\sqrt{7 - 3 x^{2}}} d x$
86022	Integrate Using u-Substitution	integral from 0 to 49 of 1/( cube root of (27+2x)^2) with respect to x	$\int_{0}^{49} \frac{1}{\sqrt[3]{{(27 + 2 x)}^{2}}} d x$
86023	Integrate Using u-Substitution	integral of xe^(-x^2) with respect to x , u=-x^2	$\int x e^{- x^{2}} d x$ , $u = - x^{2}$
86024	Integrate Using u-Substitution	integral from 0 to 1 of e^(-2x) with respect to x	$\int_{0}^{1} e^{- 2 x} d x$
86025	Integrate Using u-Substitution	integral from 0 to square root of pi of xcos(x^2) with respect to x	$\int_{0}^{\sqrt{π}} x \cos (x^{2}) d x$
86026	Integrate Using u-Substitution	integral of ((t^3)/3+1/(4t^2)) with respect to t	$\int (\frac{t^{3}}{3} + \frac{1}{4 t^{2}}) d t$
86027	Integrate Using u-Substitution	integral of sec(5x)^2 with respect to x	$\int \sec^{2} (5 x) d x$
86028	Integrate Using u-Substitution	integral of (2x)/( square root of 2x-1) with respect to x	$\int \frac{2 x}{\sqrt{2 x - 1}} d x$
86029	Integrate Using u-Substitution	integral of (9r^2)/( square root of 1-r^3) with respect to r	$\int \frac{9 r^{2}}{\sqrt{1 - r^{3}}} d r$
86030	Integrate Using u-Substitution	integral of (x^2+x) cube root of x+7 with respect to x	$\int (x^{2} + x) \sqrt[3]{x + 7} d x$
86031	Integrate Using u-Substitution	integral of sin(x)^2cos(x)^4 with respect to x	$\int \sin^{2} (x) \cos^{4} (x) d x$
86032	Integrate Using u-Substitution	integral of (sin(x))/( square root of cos(x)) with respect to x	$\int \frac{\sin (x)}{\sqrt{\cos (x)}} d x$
86033	Integrate Using u-Substitution	integral of (18x^2)/( cube root of x^3+4) with respect to x	$\int \frac{18 x^{2}}{\sqrt[3]{x^{3} + 4}} d x$
86034	Integrate Using u-Substitution	integral of 1/(ax+b) with respect to x	$\int \frac{1}{a x + b} d x$
86035	Integrate Using u-Substitution	integral from -1 to 1 of x^2 square root of x^3+1 with respect to x	$\int_{- 1}^{1} x^{2} \sqrt{x^{3} + 1} d x$
86036	Integrate Using u-Substitution	integral of square root of 3x with respect to x	$\int \sqrt{3 x} d x$
86037	Integrate Using u-Substitution	f(x) = integral of (x+1)^3 with respect to x	$f (x) = \int {(x + 1)}^{3} d x$
86038	Integrate Using u-Substitution	integral of x/(x-1) with respect to x	$\int \frac{x}{x - 1} d x$
86039	Integrate Using u-Substitution	integral of 1/(sin(x)) with respect to x	$\int \frac{1}{\sin (x)} d x$
86040	Find the Tangent Line at x=5	f(x) = square root of x^2+11 ; x=5	$f (x) = \sqrt{x^{2} + 11}$ ; $x = 5$
86041	Find the Tangent Line at (0,1)	y=e^xcos(x)+sin(x) , (0,1)	$y = e^{x} \cos (x) + \sin (x)$ , $(0, 1)$
86042	Find the Tangent Line at (1,0)	y=(x^2-1)/(x^2+x+1) , (1,0)	$y = \frac{x^{2} - 1}{x^{2} + x + 1}$ , $(1, 0)$
86043	Find the Tangent Line at (-3√(3),1)	x^(2/3)+y^(2/3)=4 , (-3 square root of 3,1)	$x^{\frac{2}{3}} + y^{\frac{2}{3}} = 4$ , $(- 3 \sqrt{3}, 1)$
86044	Find the Tangent Line at (4π,0)	y=sin(sin(x)) , (4pi,0)	$y = \sin (\sin (x))$ , $(4 π, 0)$
86045	Find the Tangent Line at (1,1)	square root of x , (1,1)	$\sqrt{x}$ , $(1, 1)$
86046	Find the Tangent Line at (3π,0)	y=sin(sin(x)) , (3pi,0)	$y = \sin (\sin (x))$ , $(3 π, 0)$
86047	Find the Tangent Line at (2π,0)	y=sin(sin(x)) , (2pi,0)	$y = \sin (\sin (x))$ , $(2 π, 0)$
86048	Find the Tangent Line at (π,0)	y=sin(sin(x)) , (pi,0)	$y = \sin (\sin (x))$ , $(π, 0)$
86049	Find the Tangent Line at (π,-1)	y=(1+sin(x))/(cos(x)) , (pi,-1)	$y = \frac{1 + \sin (x)}{\cos (x)}$ , $(π, - 1)$
86050	Find the Tangent Line at (2,1)	x^2+6xy+12y^2=28 , (2,1)	$x^{2} + 6 x y + 12 y^{2} = 28$ , $(2, 1)$
86051	Find the Tangent Line at (7,4)	f(x)=((x+1)/(x-3))^2 ; (7,4)	$f (x) = {(\frac{x + 1}{x - 3})}^{2}$ ; $(7, 4)$
86052	Find the Tangent Line at (1,-1)	(x-y-1)^3=x ; (1,-1)	${(x - y - 1)}^{3} = x$ ; $(1, - 1)$
86053	Find the Tangent Line at x=3	f(x) = square root of x^2+55 ; x=3	$f (x) = \sqrt{x^{2} + 55}$ ; $x = 3$
86054	Find the Tangent Line at (5,4)	f(x)=((x+3)/(x-1))^2 ; (5,4)	$f (x) = {(\frac{x + 3}{x - 1})}^{2}$ ; $(5, 4)$
86055	Find the Tangent Line at (6,0)	y = natural log of x^2-6x+1 , (6,0)	$y = \ln (x^{2} - 6 x + 1)$ , $(6, 0)$
86056	Find the Tangent Line at (3,0)	y = natural log of x^2-3x+1 , (3,0)	$y = \ln (x^{2} - 3 x + 1)$ , $(3, 0)$
86057	Find the Tangent Line at (2,2)	y = fifth root of 2x^3+8x , (2,2)	$y = \sqrt[5]{2 x^{3} + 8 x}$ , $(2, 2)$
86058	Find the Tangent Line at (2,0)	y = natural log of x^2-2x+1 , (2,0)	$y = \ln (x^{2} - 2 x + 1)$ , $(2, 0)$
86059	Find the Tangent Line at x=3	f(x) = square root of x^2+16 ; x=3	$f (x) = \sqrt{x^{2} + 16}$ ; $x = 3$
86060	Find the Tangent Line at (6,4)	f(x)=((x+2)/(x-2))^2 ; (6,4)	$f (x) = {(\frac{x + 2}{x - 2})}^{2}$ ; $(6, 4)$
86061	Find the Tangent Line at (π,π)	y=x+sin(x) , (pi,pi)	$y = x + \sin (x)$ , $(π, π)$
86062	Find the Tangent Line at x=7	f(x) = square root of x^2+15 ; x=7	$f (x) = \sqrt{x^{2} + 15}$ ; $x = 7$
86063	Find the Tangent Line at x=4	f(x) = square root of x^2+9 ; x=4	$f (x) = \sqrt{x^{2} + 9}$ ; $x = 4$
86064	Find the Tangent Line at x=2	f(x) = square root of x^2+21 ; x=2	$f (x) = \sqrt{x^{2} + 21}$ ; $x = 2$
86065	Find the Tangent Line at (π/3,2)	y=sec(x) , (pi/3,2)	$y = \sec (x)$ , $(\frac{π}{3}, 2)$
86066	Find the Tangent Line at (4,0)	y = natural log of x^2-4x+1 , (4,0)	$y = \ln (x^{2} - 4 x + 1)$ , $(4, 0)$
86067	Find the Tangent Line at x=5	f(x) = square root of x^2+39 ; x=5	$f (x) = \sqrt{x^{2} + 39}$ ; $x = 5$
86068	Find the Tangent Line at (0,1)	f(x)=3x^2-12x+1 at the point (0,1)	$f (x) = 3 x^{2} - 12 x + 1$ at the point $(0, 1)$
86069	Find the Tangent Line at (9,0)	y = natural log of x^2-9x+1 , (9,0)	$y = \ln (x^{2} - 9 x + 1)$ , $(9, 0)$
86070	Find the Tangent Line at (0,1)	y=e^xcos(x)+sin(x) , (0,1)	$y = e^{x} \cos (x) + \sin (x)$ , $(0, 1)$
86071	Find the Tangent Line at (8,0)	y = natural log of x^2-8x+1 , (8,0)	$y = \ln (x^{2} - 8 x + 1)$ , $(8, 0)$
86072	Find the Tangent Line at (7,0)	y = natural log of x^2-7x+1 , (7,0)	$y = \ln (x^{2} - 7 x + 1)$ , $(7, 0)$
86073	Find the Tangent Line at x=1	f(x) = natural log of 1-x^2+2x^4 ; x=1	$f (x) = \ln (1 - x^{2} + 2 x^{4})$ ; $x = 1$
86074	Find the Tangent Line at (1/2,π/2)	y=3arcsin(x) , (1/2,pi/2)	$y = 3 \arcsin (x)$ , $(\frac{1}{2}, \frac{π}{2})$
86075	Find the Tangent Line at (-1,2)	y^2=5x^4-x^2 , (-1,2)	$y^{2} = 5 x^{4} - x^{2}$ , $(- 1, 2)$
86076	Find the Tangent Line at (5,0)	y = natural log of x^2-5x+1 , (5,0)	$y = \ln (x^{2} - 5 x + 1)$ , $(5, 0)$
86077	Find the Tangent Line at (9,18)	y=6 square root of x , (9,18)	$y = 6 \sqrt{x}$ , $(9, 18)$
86078	Find the Tangent Line at (0,1)	y=sin(x)+cos(x) , (0,1)	$y = \sin (x) + \cos (x)$ , $(0, 1)$
86079	Find the Tangent Line at (2,4)	y=x^3-3x+2 , (2,4)	$y = x^{3} - 3 x + 2$ , $(2, 4)$
86080	Find the Tangent Line at (1.5,2.25)	x^2 , (1.5,2.25)	$x^{2}$ , $(1.5, 2.25)$
86081	Find the Tangent Line at (1,3)	y=4x^2-x^3 , (1,3)	$y = 4 x^{2} - x^{3}$ , $(1, 3)$
86082	Find the Tangent Line at x=1	f(x) = natural log of 2-x^2+2x^4 ; x=1	$f (x) = \ln (2 - x^{2} + 2 x^{4})$ ; $x = 1$
86083	Find the Tangent Line at (25,5)	y = square root of x , (25,5)	$y = \sqrt{x}$ , $(25, 5)$
86084	Find the Tangent Line at (4,2)	y = square root of x , (4,2)	$y = \sqrt{x}$ , $(4, 2)$
86085	Find the Tangent Line at (-1,1/2)	y=1/(1+x^2) , (-1,1/2)	$y = \frac{1}{1 + x^{2}}$ , $(- 1, \frac{1}{2})$
86086	Find the Tangent Line at (π/4,1)	f(x)=tan(x)^2 , (pi/4,1)	$f (x) = \tan^{2} (x)$ , $(\frac{π}{4}, 1)$
86087	Find the Tangent Line at (-π/4,1)	f(x)=tan(x)^2 , (-pi/4,1)	$f (x) = \tan^{2} (x)$ , $(- \frac{π}{4}, 1)$
86088	Find the Tangent Line at x=4	f(x)=( square root of x+1)/( square root of x+5) ; x=4	$f (x) = \frac{\sqrt{x} + 1}{\sqrt{x} + 5}$ ; $x = 4$
86089	Find the Tangent Line at (3π,0)	y=sin(sin(x)) , (3pi,0)	$y = \sin (\sin (x))$ , $(3 π, 0)$
86090	Find the Tangent Line at (0,0)	ye^(sin(x))=xcos(y) , (0,0)	$y e^{\sin (x)} = x \cos (y)$ , $(0, 0)$
86091	Find the Tangent Line at (1,-5)	f(x)=(x-2)(x^2+4) , (1,-5)	$f (x) = (x - 2) (x^{2} + 4)$ , $(1, - 5)$
86092	Find the Tangent Line at (3,19)	y=x^3-3x+1 , (3,19)	$y = x^{3} - 3 x + 1$ , $(3, 19)$
86093	Find the Tangent Line at (1,0)	f(x)=(x^2-1)/(x^2+x+1) , (1,0)	$f (x) = \frac{x^{2} - 1}{x^{2} + x + 1}$ , $(1, 0)$
86094	Find the Tangent Line at (2π,0)	y=sin(sin(x)) , (2pi,0)	$y = \sin (\sin (x))$ , $(2 π, 0)$
86095	Find the Tangent Line at (π,0)	y=sin(sin(x)) , (pi,0)	$y = \sin (\sin (x))$ , $(π, 0)$
86096	Find the Tangent Line at (4,53)	y=x^3-3x+1 , (4,53)	$y = x^{3} - 3 x + 1$ , $(4, 53)$
86097	Find the Tangent Line at (π/6,2√(3)/3)	y=sec(x) , (pi/6,(2 square root of 3)/3)	$y = \sec (x)$ , $(\frac{π}{6}, \frac{2 \sqrt{3}}{3})$
86098	Find the Tangent Line at x=2	f(x)=(8x-7)^(1/2) , x=2	$f (x) = {(8 x - 7)}^{\frac{1}{2}}$ , $x = 2$
86099	Find the Tangent Line at (1,0)	x^2-xy-y^2=1 , (1,0)	$x^{2} - x y - y^{2} = 1$ , $(1, 0)$
86100	Find the Tangent Line at (9,54)	y=18 square root of x , (9,54)	$y = 18 \sqrt{x}$ , $(9, 54)$