Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
82001	Find the Antiderivative	f(x)=(3x+2)^4-1/(x^6)	$f (x) = {(3 x + 2)}^{4} - \frac{1}{x^{6}}$
82002	Find the Absolute Max and Min over the Interval	-3+4i	$- 3 + 4 i$
82003	Integrate Using u-Substitution	integral of x^2 square root of x^3+1 with respect to x , u=x^3+1	$\int x^{2} \sqrt{x^{3} + 1} d x$ , $u = x^{3} + 1$
82004	Find the Antiderivative	e/x	$\frac{e}{x}$
82005	Integrate Using u-Substitution	integral of 3/((3-2x)^2) with respect to x	$\int \frac{3}{{(3 - 2 x)}^{2}} d x$
82006	Find the Antiderivative	e^(2x)+1	$e^{2 x} + 1$
82007	Find the Derivative - d/dx	(x-6)/(4x)	$\frac{x - 6}{4 x}$
82008	Find the Concavity	f(x)=arctan(x^2)	$f (x) = \arctan (x^{2})$
82009	Evaluate Using L'Hospital's Rule	limit as x approaches 0 of (cos(3x)-1)/(e^(-x)-1)	$lim_{x \to 0} \frac{\cos (3 x) - 1}{e^{- x} - 1}$
82010	Find the Antiderivative	(2x-1)e^x	$(2 x - 1) e^{x}$
82011	Integrate Using u-Substitution	integral of 1/(1+x^2) with respect to x	$\int \frac{1}{1 + x^{2}} d x$
82012	Find the Third Derivative	f(x)=5/8x^-2+4/3x^3+2/3x^4+1/10x^-3	$f (x) = \frac{5}{8} x^{- 2} + \frac{4}{3} x^{3} + \frac{2}{3} x^{4} + \frac{1}{10} x^{- 3}$
82013	Find the Derivative - d/dx	4x^2e^(-x^2)-2e^(-x^2)	$4 x^{2} e^{- x^{2}} - 2 e^{- x^{2}}$
82014	Find dy/dx	y^3+4x^2+1=-5x-3y	$y^{3} + 4 x^{2} + 1 = - 5 x - 3 y$
82015	Find the Derivative - d/dx	(x^2-x-11)/(e^x)	$\frac{x^{2} - x - 11}{e^{x}}$
82016	Evaluate the Integral	integral of ( square root of x^4- fifth root of x^8) with respect to x	$\int (\sqrt{x^{4}} - \sqrt[5]{x^{8}}) d x$
82017	Find the Derivative - d/dx	2e^x-x+5sin(x)-12	$2 e^{x} - x + 5 \sin (x) - 12$
82018	Evaluate the Limit	limit as x approaches negative infinity of (5x)/(x^2-10x+3)	$lim_{x \to - \infty} \frac{5 x}{x^{2} - 10 x + 3}$
82019	Find Where Increasing/Decreasing	f(x)=- natural log of x+5	$f (x) = - \ln (x + 5)$
82020	Evaluate the Limit	limit as x approaches 0 of (sin(1/2x))/x	$lim_{x \to 0} \frac{\sin (\frac{1}{2} x)}{x}$
82021	Find dy/dx	xy-2x^2-y=-3	$x y - 2 x^{2} - y = - 3$
82022	Find the Antiderivative	3/( cube root of 2x-1)	$\frac{3}{\sqrt[3]{2 x - 1}}$
82023	Find dy/dx	(x^3+3y)^5=4y^3	${(x^{3} + 3 y)}^{5} = 4 y^{3}$
82024	Find the Derivative - d/dx	((x+1)^2)/(x^2+8)	$\frac{{(x + 1)}^{2}}{x^{2} + 8}$
82025	Find the Derivative Using Chain Rule - d/dx	y=((x-5)/(2x+1))^3	$y = {(\frac{x - 5}{2 x + 1})}^{3}$
82026	Evaluate the Integral	integral of sin(x)^2*cos(x) with respect to x	$\int \sin^{2} (x) \cdot \cos (x) d x$
82027	Find the Derivative - d/dx	cos(pi/2x)	$\cos (\frac{π}{2} x)$
82028	Find the Maximum/Minimum Value	y=x^3+x^2-8x+5	$y = x^{3} + x^{2} - 8 x + 5$
82029	Evaluate the Integral	integral of 2x(x^2-3)(1/2) with respect to x	$\int 2 x (x^{2} - 3) (\frac{1}{2}) d x$
82030	Find the Antiderivative	e^(ax)	$e^{a x}$
82031	Find dy/dx	-5y+4x^3y+2x^2=0	$- 5 y + 4 x^{3} y + 2 x^{2} = 0$
82032	Find the Antiderivative	3x^2+sin(x)	$3 x^{2} + \sin (x)$
82033	Find dy/dx	2+y^2+3y=-x^2+2x^3	$2 + y^{2} + 3 y = - x^{2} + 2 x^{3}$
82034	Find the Second Derivative	natural log of sin(x)	$\ln (\sin (x))$
82035	Find the Antiderivative	f(x)=1/( cube root of x)	$f (x) = \frac{1}{\sqrt[3]{x}}$
82036	Evaluate the Limit	limit as x approaches 7 from the right of 3/(x-7)- natural log of x-7	$lim_{x \to 7^{+}} \frac{3}{x - 7} - \ln (x - 7)$
82037	Find dQ/dL	Q=5L+6LK^2+8K	$Q = 5 L + 6 L K^{2} + 8 K$
82038	Find the Antiderivative	(6x+2)/(3x-1)	$\frac{6 x + 2}{3 x - 1}$
82039	Find the Linearization at θ=0	f(theta)=cos(theta+pi/3) , theta=0	$f (θ) = \cos (θ + \frac{π}{3})$ , $θ = 0$
82040	Find dy/dx	y=(x^2+3)^2(x^2+5)^3	$y = {(x^{2} + 3)}^{2} {(x^{2} + 5)}^{3}$
82041	Find dy/dx	-4-x=y^3+xy	$- 4 - x = y^{3} + x y$
82042	Find the Antiderivative	(sin(2x)-cos(2x))^2	${(\sin (2 x) - \cos (2 x))}^{2}$
82043	Evaluate the Limit	limit as x approaches -3 of (3x^2-x)/(x+4)	$lim_{x \to - 3} \frac{3 x^{2} - x}{x + 4}$
82044	Evaluate the Limit	limit as x approaches 0 of (5-5cos(x))/x	$lim_{x \to 0} \frac{5 - 5 \cos (x)}{x}$
82045	Find dy/dx	5y^2+5+x^3=y^3	$5 y^{2} + 5 + x^{3} = y^{3}$
82046	Integrate Using u-Substitution	integral of (1-2x)^9 with respect to x	$\int {(1 - 2 x)}^{9} d x$
82047	Evaluate the Integral	integral of (2sin(2x))/(1+9cos(2x)^2) with respect to x	$\int \frac{2 \sin (2 x)}{1 + 9 \cos^{2} (2 x)} d x$
82048	Find the Antiderivative	x/y	$\frac{x}{y}$
82049	Find the Derivative - d/dx	natural log of 2e^x-1	$\ln (2 e^{x} - 1)$
82050	Evaluate the Summation	sum from i=-2 to 3 of 3^(-i)	$\sum_{i = - 2}^{3} 3^{- i}$
82051	Find the Second Derivative	y=xe^(-x^2)	$y = x e^{- x^{2}}$
82052	Evaluate the Integral	integral from 1 to 9 of ((x-2)/( square root of x)) with respect to x	$\int_{1}^{9} (\frac{x - 2}{\sqrt{x}}) d x$
82053	Evaluate the Limit	limit as x approaches 1 of (3-f(x))/(1-4g(x))	$lim_{x \to 1} \frac{3 - f (x)}{1 - 4 g (x)}$
82054	Find the Integral	xe^(x^2)dx	$x e^{x^{2}} d x$
82055	Find dz/dx	z=(2x^(1/3)+y^(1/2))^3	$z = {(2 x^{\frac{1}{3}} + y^{\frac{1}{2}})}^{3}$
82056	Integrate Using u-Substitution	integral of x square root of x^2+1 with respect to x	$\int x \sqrt{x^{2} + 1} d x$
82057	Integrate Using Partial Fractions	integral of x/(x-6) with respect to x	$\int \frac{x}{x - 6} d x$
82058	Find Where Increasing/Decreasing	f(x)=x natural log of x	$f (x) = x \ln (x)$
82059	Find the Antiderivative	(x+1)(x+2)(x+3)	$(x + 1) (x + 2) (x + 3)$
82060	Evaluate the Limit	limit as x approaches -1 of (x^3-5x+7)/(1-x+x^2-x^3)	$lim_{x \to - 1} \frac{x^{3} - 5 x + 7}{1 - x + x^{2} - x^{3}}$
82061	Evaluate the Integral	integral of (cos(x)+3x^2) with respect to x	$\int (\cos (x) + 3 x^{2}) d x$
82062	Evaluate the Limit	limit as x approaches 0 of (2x^2+x)/(5x)	$lim_{x \to 0} \frac{2 x^{2} + x}{5 x}$
82063	Find dy/dx	-y^2+y-x^2+y^3=1	$- y^{2} + y - x^{2} + y^{3} = 1$
82064	Find dy/dx	-y^3+y^2=x^2	$- y^{3} + y^{2} = x^{2}$
82065	Integrate Using u-Substitution	integral of (e^(arcsin(x)))/( square root of 1-x^2) with respect to x	$\int \frac{e^{\arcsin (x)}}{\sqrt{1 - x^{2}}} d x$
82066	Find the Integral	x square root of x^2+9	$x \sqrt{x^{2} + 9}$
82067	Evaluate the Integral	integral of 1/2+3/4x^2-4/5x^3 with respect to x	$\int \frac{1}{2} + \frac{3}{4} x^{2} - \frac{4}{5} x^{3} d x$
82068	Find the Derivative Using Product Rule - d/dx	xcos(x)	$x \cos (x)$
82069	Evaluate the Integral	integral from 1 to 2 of (e^(2x^-2))/(x^3) with respect to x	$\int_{1}^{2} \frac{e^{2 x^{- 2}}}{x^{3}} d x$
82070	Find dy/dx	-2x-3y^2=1+xy	$- 2 x - 3 y^{2} = 1 + x y$
82071	Evaluate the Integral	If integral from 0 to a of 3x^2 with respect to x=1	If $\int_{0}^{a} 3 x^{2} d x = 1$
82072	Find the Derivative - d/dx	( square root of 3x^2)/2	$\frac{\sqrt{3 x^{2}}}{2}$
82073	Evaluate the Integral	integral from 0 to x^3 of f(8) with respect to t=x^4	$\int_{0}^{x^{3}} f (8) d t = x^{4}$
82074	Find the Maximum/Minimum Value	f(x)=x^4-x^2+x	$f (x) = x^{4} - x^{2} + x$
82075	Find dy/dx	-5x^3-y^3+1=0	$- 5 x^{3} - y^{3} + 1 = 0$
82076	Evaluate the Integral	integral of x^2(4x-3)(2x+1) with respect to x	$\int x^{2} (4 x - 3) (2 x + 1) d x$
82077	Evaluate the Integral	integral of (2-6 square root of x)/(8 fourth root of x) with respect to x	$\int \frac{2 - 6 \sqrt{x}}{8 \sqrt[4]{x}} d x$
82078	Evaluate the Integral	integral of (4sin(x))/(3+cos(x)) with respect to x	$\int \frac{4 \sin (x)}{3 + \cos (x)} d x$
82079	Evaluate the Limit	limit as x approaches 3 of (x^3-4x^2+3x)/(9-x^2)	$lim_{x \to 3} \frac{x^{3} - 4 x^{2} + 3 x}{9 - x^{2}}$
82080	Find the Derivative - d/dh	(h^3-5)(3h^2-5h-4)	$(h^{3} - 5) (3 h^{2} - 5 h - 4)$
82081	Find the Derivative - d/dx	e^(e^(x^2))	$e^{e^{x^{2}}}$
82082	Find Where Increasing/Decreasing	x+1/x	$x + \frac{1}{x}$
82083	Find dy/dx	y=(7^x)/2	$y = \frac{7^{x}}{2}$
82084	Find the Antiderivative	(5+2x^4)/(x^2)	$\frac{5 + 2 x^{4}}{x^{2}}$
82085	Find the Antiderivative	2^( square root of x)*( natural log of 2)/( square root of x)	$2^{\sqrt{x}} \cdot \frac{\ln (2)}{\sqrt{x}}$
82086	Evaluate the Integral	integral of (x+2x^2+3x^3)/x with respect to x	$\int \frac{x + 2 x^{2} + 3 x^{3}}{x} d x$
82087	Find the Maximum/Minimum Value	f(x)=3/4x^4-3x^3-81x^2-16	$f (x) = \frac{3}{4} x^{4} - 3 x^{3} - 81 x^{2} - 16$
82088	Find Where Increasing/Decreasing	f(x)=1/3x^3-3x^2-16x	$f (x) = \frac{1}{3} x^{3} - 3 x^{2} - 16 x$
82089	Find the Antiderivative	(e^(-x))^2	${(e^{- x})}^{2}$
82090	Find the Derivative - d/dx	y=12/18x^18-15x^2	$y = \frac{12}{18} x^{18} - 15 x^{2}$
82091	Find the Derivative - d/dx	y=x/z	$y = \frac{x}{z}$
82092	Evaluate the Limit	limit as x approaches 3 from the right of (x-3)/(\|x^3-3x^2\|) is	$lim_{x \to 3^{+}} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$ is
82093	Find the Antiderivative	(tan(x)+cot(x))^2	${(\tan (x) + \cot (x))}^{2}$
82094	Find the Derivative - d/dx	pisec(x)	$π \sec (x)$
82095	Find the Antiderivative	x-1/x	$x - \frac{1}{x}$
82096	Find the Derivative - d/dx	d/(dx)(4+(f(8x)))^3	$\frac{d}{d x} {(4 + (f (8 x)))}^{3}$
82097	Evaluate the Integral	integral of (1/x-6/(x^2+1)) with respect to x	$\int (\frac{1}{x} - \frac{6}{x^{2} + 1}) d x$
82098	Evaluate the Limit	limit as x approaches natural log of 10 of e^x+3	$lim_{x \to \ln (10)} e^{x} + 3$
82099	Evaluate the Limit	limit as x approaches 3 from the left of (x-3)/(\|x^3-3x^2\|) is	$lim_{x \to 3^{-}} \frac{x - 3}{\| x^{3} - 3 x^{2} \|}$ is
82100	Find dy/dx	y=(x-6)/(4x)	$y = \frac{x - 6}{4 x}$