Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
80901	Evaluate the Integral	integral of (2/3x^5-5/2x+1/2) with respect to x	$\int (\frac{2}{3} x^{5} - \frac{5}{2} x + \frac{1}{2}) d x$
80902	Integrate Using u-Substitution	integral of x/((x^2+1)^2) with respect to x	$\int \frac{x}{{(x^{2} + 1)}^{2}} d x$
80903	Find Where Increasing/Decreasing	f(x) = cube root of x-2+7	$f (x) = \sqrt[3]{x - 2} + 7$
80904	Find the Inflection Points	f(x)=1/10x^5-x^4	$f (x) = \frac{1}{10} x^{5} - x^{4}$
80905	Find the Antiderivative	2cos(x/2)^2	$2 \cos^{2} (\frac{x}{2})$
80906	Evaluate the Integral	integral of (5xe^(3x^2))/( square root of 2-3e^(3x^2)) with respect to x	$\int \frac{5 x e^{3 x^{2}}}{\sqrt{2 - 3 e^{3 x^{2}}}} d x$
80907	Evaluate the Integral	integral from e to infinity of 1/(x( natural log of 2x)^3) with respect to x	$\int_{e}^{\infty} \frac{1}{x \ln^{3} (2 x)} d x$
80908	Find the Derivative - d/dx	y=2csc(1-3x)	$y = 2 \csc (1 - 3 x)$
80909	Find the Antiderivative	(2x)/(1+x^2)	$\frac{2 x}{1 + x^{2}}$
80910	Find the Antiderivative	x^2+ square root of x	$x^{2} + \sqrt{x}$
80911	Find Where Increasing/Decreasing	f(x)=-2*2^(1/3x)+3	$f (x) = - 2 \cdot 2^{\frac{1}{3} x} + 3$
80912	Find the Maximum/Minimum Value	y=3sin(3/4)(x+(2pi)/3)-5	$y = 3 \sin (\frac{3}{4}) (x + \frac{2 π}{3}) - 5$
80913	Find the Concavity	f(x)=x^(2/3)-4x^(1/3)	$f (x) = x^{\frac{2}{3}} - 4 x^{\frac{1}{3}}$
80914	Find the Derivative - d/dx	-(x+1)(x-1)^2	$- (x + 1) {(x - 1)}^{2}$
80915	Find the Derivative - d/dx	x^2e^(kx)	$x^{2} e^{k x}$
80916	Evaluate the Limit	limit as x approaches 1 of ((x-3)(x^2-2))/(x^2+1)	$lim_{x \to 1} \frac{(x - 3) (x^{2} - 2)}{x^{2} + 1}$
80917	Evaluate the Integral	integral of (sec(theta)^2-sin(theta)) with respect to theta	$\int (\sec^{2} (θ) - \sin (θ)) d θ$
80918	Evaluate the Integral	integral of (x^-7+x^(-1/3)+x^-2) with respect to x	$\int (x^{- 7} + x^{- \frac{1}{3}} + x^{- 2}) d x$
80919	Evaluate the Summation	sum from k=5 to 12 of (-1)^k*2k	$\sum_{k = 5}^{12} {(- 1)}^{k} \cdot 2 k$
80920	Find the Derivative - d/dx	-5x^(-1/2)	$- 5 x^{- \frac{1}{2}}$
80921	Find the Local Maxima and Minima	f(x)=-3/5x^5+9x^4-35x^3+6	$f (x) = - \frac{3}{5} x^{5} + 9 x^{4} - 35 x^{3} + 6$
80922	Find the Concavity	f(x)=1/10x^5+2x^4+12x^3	$f (x) = \frac{1}{10} x^{5} + 2 x^{4} + 12 x^{3}$
80923	Evaluate the Integral	integral of 2xe^(-2x) with respect to x	$\int 2 x e^{- 2 x} d x$
80924	Find the Derivative - d/dx	y = square root of 5-2e^(3x)	$y = \sqrt{5 - 2 e^{3 x}}$
80925	Evaluate the Integral	integral from 0 to infinity of x^2e^(-x^3) with respect to x	$\int_{0}^{\infty} x^{2} e^{- x^{3}} d x$
80926	Evaluate the Integral	integral from 0 to 2 of (4x+5)e^(-x) with respect to x	$\int_{0}^{2} (4 x + 5) e^{- x} d x$
80927	Find the Maximum/Minimum Value	xe^x	$x e^{x}$
80928	Evaluate the Limit	limit as x approaches negative infinity of (4x^3+6x^2-2)/(5-4x+2x^2)	$lim_{x \to - \infty} \frac{4 x^{3} + 6 x^{2} - 2}{5 - 4 x + 2 x^{2}}$
80929	Evaluate the Integral	integral from 0 to 3 of 3/2 square root of x+1 with respect to x	$\int_{0}^{3} \frac{3}{2} \sqrt{x + 1} d x$
80930	Integrate Using u-Substitution	integral of 1/(x^2) with respect to x	$\int \frac{1}{x^{2}} d x$
80931	Find the Inflection Points	f(x)=-1/6x^6-x^5-5/3x^4	$f (x) = - \frac{1}{6} x^{6} - x^{5} - \frac{5}{3} x^{4}$
80932	Find dy/dx	y=((x^2)/(6x^3-6))^5	$y = {(\frac{x^{2}}{6 x^{3} - 6})}^{5}$
80933	Evaluate the Integral	integral of 3x(3x+2)(4x-1) with respect to x	$\int 3 x (3 x + 2) (4 x - 1) d x$
80934	Find the Derivative - d/dx	y=arctanh(1-2x)	$y = arctanh (1 - 2 x)$
80935	Find the Derivative - d/dx	square root of 3x^3	$\sqrt{3 x^{3}}$
80936	Evaluate the Integral	integral from 1 to 2 of (x+1)e^(-2x) with respect to x	$\int_{1}^{2} (x + 1) e^{- 2 x} d x$
80937	Find the Antiderivative	-(x^2)/2	$- \frac{x^{2}}{2}$
80938	Evaluate the Integral	integral of (3 natural log of x)/(2x) with respect to x	$\int \frac{3 \ln (x)}{2 x} d x$
80939	Find the Percentage Rate of Change	g(t)=2(5/4)^t	$g (t) = 2 {(\frac{5}{4})}^{t}$
80940	Evaluate the Integral	integral of ( square root of x)/2 with respect to x	$\int \frac{\sqrt{x}}{2} d x$
80941	Find the Derivative - d/dx	y=cos(x)^2-sin(x)^2	$y = \cos^{2} (x) - \sin^{2} (x)$
80942	Evaluate the Integral	integral from 0 to 1 of (x+1)/(x^2+2x-3) with respect to x	$\int_{0}^{1} \frac{x + 1}{x^{2} + 2 x - 3} d x$
80943	Find the Antiderivative	f(x)=3/(2x-5)-4	$f (x) = \frac{3}{2 x - 5} - 4$
80944	Evaluate the Limit	limit as x approaches 8 of ( square root of 12-x-2)/( square root of 24-x-4)	$lim_{x \to 8} \frac{\sqrt{12 - x} - 2}{\sqrt{24 - x} - 4}$
80945	Find the Inflection Points	f(x)=1/4x^4+x^3+3/2x^2	$f (x) = \frac{1}{4} x^{4} + x^{3} + \frac{3}{2} x^{2}$
80946	Evaluate the Limit	limit as x approaches 10 of \|-x-5\|	$lim_{x \to 10} \| - x - 5 \|$
80947	Find the Derivative - d/dx	y=(8x^3)/16	$y = \frac{8 x^{3}}{16}$
80948	Find the Integral	x/(x-1)	$\frac{x}{x - 1}$
80949	Find the Derivative - d/dx	y=(3x^4-7)*(5x^2+1)	$y = (3 x^{4} - 7) \cdot (5 x^{2} + 1)$
80950	Evaluate the Limit	limit as x approaches 4 of (3x-12)/(4-x)	$lim_{x \to 4} \frac{3 x - 12}{4 - x}$
80951	Find the Derivative - d/dx	y=arctan( square root of x-7)	$y = \arctan (\sqrt{x - 7})$
80952	Find the Antiderivative	square root of x^2+8x+6	$\sqrt{x^{2} + 8 x + 6}$
80953	Find the Derivative - d/dx	e^x-e	$e^{x} - e$
80954	Integrate Using Trig Substitution	integral of cos(x)^3sin(x)^2 with respect to x	$\int \cos^{3} (x) \sin^{2} (x) d x$
80955	Evaluate the Limit	limit as x approaches c of (27)^(2/3)	$lim_{x \to c} {(27)}^{\frac{2}{3}}$
80956	Find dy/dx	y=9^(1-x^2)	$y = 9^{1 - x^{2}}$
80957	Evaluate the Integral	integral of square root of x^2+8x+6 with respect to x	$\int \sqrt{x^{2} + 8 x + 6} d x$
80958	Find Where Increasing/Decreasing	y=1/3*5^x	$y = \frac{1}{3} \cdot 5^{x}$
80959	Find the Derivative - d/dx	y=(3x^2)^4	$y = {(3 x^{2})}^{4}$
80960	Find Where Increasing/Decreasing	f(x)=-3/5x^5-6x^4-15x^3-1	$f (x) = - \frac{3}{5} x^{5} - 6 x^{4} - 15 x^{3} - 1$
80961	Find the Antiderivative	square root of x^2	$\sqrt{x^{2}}$
80962	Evaluate the Integral	integral of (1-csc(t)cot(t)) with respect to t	$\int (1 - \csc (t) \cot (t)) d t$
80963	Evaluate the Integral	integral of -1/2x^3 with respect to x	$\int - \frac{1}{2} x^{3} d x$
80964	Find the Concavity	f(x)=1/5x^5-x^4-12x^3	$f (x) = \frac{1}{5} x^{5} - x^{4} - 12 x^{3}$
80965	Find Where Increasing/Decreasing	f(x)=-x^4-4x^3-2x^2+3x-1	$f (x) = - x^{4} - 4 x^{3} - 2 x^{2} + 3 x - 1$
80966	Find the Derivative - d/dx	1+2xe^y	$1 + 2 x e^{y}$
80967	Find dy/dx	y=arcsec(cos(2x))	$y = arcsec (\cos (2 x))$
80968	Find the Antiderivative	4+x	$4 + x$
80969	Find the Maximum/Minimum Value	f(x)=e^(-x)(x^2+2x)	$f (x) = e^{- x} (x^{2} + 2 x)$
80970	Find dy/dx	-y-5y^3=5x^3	$- y - 5 y^{3} = 5 x^{3}$
80971	Find the Concavity	f(x)=-x^5+5x^4	$f (x) = - x^{5} + 5 x^{4}$
80972	Find the Second Derivative	y=x^4+1/2x^-3+3/10x^6-1/2x^2	$y = x^{4} + \frac{1}{2} x^{- 3} + \frac{3}{10} x^{6} - \frac{1}{2} x^{2}$
80973	Find the Antiderivative	x/(1-x^2)	$\frac{x}{1 - x^{2}}$
80974	Find the Derivative - d/dx	y=3x(x^3-1)	$y = 3 x (x^{3} - 1)$
80975	Find the Antiderivative	f(x)=2/(x^3)-3/x	$f (x) = \frac{2}{x^{3}} - \frac{3}{x}$
80976	Evaluate the Limit	limit as x approaches infinity of (x^2+5)/6	$lim_{x \to \infty} \frac{x^{2} + 5}{6}$
80977	Find the Concavity	f(x)=3/20x^5-2x^4+8x^3	$f (x) = \frac{3}{20} x^{5} - 2 x^{4} + 8 x^{3}$
80978	Find dy/dx	natural log of y+x/y=2021	$\ln (y) + \frac{x}{y} = 2021$
80979	Find the Derivative - d/dx	-2 square root of sin(x)	$- 2 \sqrt{\sin (x)}$
80980	Find dy/dx	y=1-xe^y	$y = 1 - x e^{y}$
80981	Find the Derivative - d/dx	integral from -2 to 2 of (x^3cos(x/2)+1/2) square root of 4-x^2dx with respect to x	$\int_{- 2}^{2} (x^{3} \cos (\frac{x}{2}) + \frac{1}{2}) \sqrt{4 - x^{2} d x} d x$
80982	Find the Inflection Points	f(x)=1/15x^6-x^4	$f (x) = \frac{1}{15} x^{6} - x^{4}$
80983	Evaluate the Integral	integral of 5e^5x with respect to x	$\int 5 e^{5} x d x$
80984	Find the Third Derivative	5x^2(x+47)	$5 x^{2} (x + 47)$
80985	Find the Antiderivative	x*sin(x)	$x \cdot \sin (x)$
80986	Find the Derivative - d/dx	square root of x^2+3-2	$\sqrt{x^{2} + 3} - 2$
80987	Find the Derivative - d/dx	x+3(1-x)^(1/3)	$x + 3 {(1 - x)}^{\frac{1}{3}}$
80988	Find the Maximum/Minimum Value	f(x)=(x^2-4)^(2/3)	$f (x) = {(x^{2} - 4)}^{\frac{2}{3}}$
80989	Evaluate the Integral	integral of ((4+2 square root of x)^2)/( square root of x) with respect to x	$\int \frac{{(4 + 2 \sqrt{x})}^{2}}{\sqrt{x}} d x$
80990	Find the Antiderivative	f(x)=2/((3x+2)^5)	$f (x) = \frac{2}{{(3 x + 2)}^{5}}$
80991	Evaluate the Integral	integral of ((x^3+2x^2-4)/(x^2)) with respect to x	$\int (\frac{x^{3} + 2 x^{2} - 4}{x^{2}}) d x$
80992	Find the Antiderivative	f(x)=-2x+6x^9-0.5	$f (x) = - 2 x + 6 x^{9} - 0.5$
80993	Evaluate the Integral	integral from 1 to 3 of (2+ye^y)/y with respect to y	$\int_{1}^{3} \frac{2 + y e^{y}}{y} d y$
80994	Find dy/dx	-3-y^3=5xy	$- 3 - y^{3} = 5 x y$
80995	Evaluate the Integral	integral of cos(x)* cube root of sin(x) with respect to x	$\int \cos (x) \cdot \sqrt[3]{\sin (x)} d x$
80996	Evaluate the Summation	sum from i=5 to 9 of i/(x+i)	$\sum_{i = 5}^{9} \frac{i}{x + i}$
80997	Find the Inflection Points	h(x)=x^5+5x^4	$h (x) = x^{5} + 5 x^{4}$
80998	Find the Maximum/Minimum Value	y=4x^3-3x^2	$y = 4 x^{3} - 3 x^{2}$
80999	Find the Derivative - d/dz	y = fifth root of z	$y = \sqrt[5]{z}$
81000	Evaluate the Limit	limit as x approaches -3 of -3/(x^2)	$lim_{x \to - 3} - \frac{3}{x^{2}}$