Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
81601	Evaluate the Integral	integral of (cos(x)-1)/x with respect to x	$\int \frac{\cos (x) - 1}{x} d x$
81602	Find the Integral	x^3e^(x^2)	$x^{3} e^{x^{2}}$
81603	Evaluate the Limit	limit as x approaches 1/2 of 4x	$lim_{x \to \frac{1}{2}} 4 x$
81604	Integrate Using u-Substitution	integral of x natural log of x with respect to x	$\int x \ln (x) d x$
81605	Find dr/dx	r = square root of x^2+y^2	$r = \sqrt{x^{2} + y^{2}}$
81606	Integrate Using u-Substitution	integral of cos(theta)^3sin(theta) with respect to theta	$\int \cos^{3} (θ) \sin (θ) d θ$
81607	Find the Derivative - d/dx	natural log of x^2 square root of 1+x^2	$\ln (x^{2} \sqrt{1 + x^{2}})$
81608	Evaluate the Integral	integral from 0 to 2 of x^2 square root of 1+x^3 with respect to x	$\int_{0}^{2} x^{2} \sqrt{1 + x^{3}} d x$
81609	Find dy/dx	4+x-y^2=-x^3y	$4 + x - y^{2} = - x^{3} y$
81610	Find the Derivative - d/dx	(x-1)*e^x	$(x - 1) \cdot e^{x}$
81611	Find the Antiderivative	x-sin(2x)	$x - \sin (2 x)$
81612	Find the Derivative - d/dx	(-cos(x))	$(- \cos (x))$
81613	Evaluate the Limit	limit as x approaches -2 of (2x^2+3x+1)^4	$lim_{x \to - 2} {(2 x^{2} + 3 x + 1)}^{4}$
81614	Find the Antiderivative	natural log of x+ square root of x^2+1	$\ln (x + \sqrt{x^{2} + 1})$
81615	Find the Antiderivative	f(x)=(x^6-x)/(x^3)	$f (x) = \frac{x^{6} - x}{x^{3}}$
81616	Find the Antiderivative	f(x)=sin(x)^2+cos(x)^2	$f (x) = \sin^{2} (x) + \cos^{2} (x)$
81617	Find dx/dy	xy+x^3=y^2	$x y + x^{3} = y^{2}$
81618	Find the Volume	y=3/(1+x) , y=0 , x=0 , x=3	$y = \frac{3}{1 + x}$ , $y = 0$ , $x = 0$ , $x = 3$
81619	Find the Derivative - d/dx	y=302.2((103^x)/(100^x))	$y = 302.2 (\frac{103^{x}}{100^{x}})$
81620	Evaluate the Integral	integral of ((-x^2+x)/(x^4)) with respect to x	$\int (\frac{- x^{2} + x}{x^{4}}) d x$
81621	Evaluate the Integral	integral of (tan( natural log of x^2))/(4x) with respect to x	$\int \frac{\tan (\ln (x^{2}))}{4 x} d x$
81622	Find the Derivative - d/dx	2^(-tan(3x))	$2^{- \tan (3 x)}$
81623	Find the Antiderivative	e^(1-3x)	$e^{1 - 3 x}$
81624	Find the Derivative - d/dt	natural log of 2t^4e^(-t)	$\ln (2 t^{4} e^{- t})$
81625	Find the Skew	3 , 4 , 4 , 5 , 17	$3$ , $4$ , $4$ , $5$ , $17$
81626	Find dy/dx	5xy+y-x-3=0	$5 x y + y - x - 3 = 0$
81627	Evaluate Using Summation Formulas	sum from i=1 to 7 of (3i-2)^2	$\sum_{i = 1}^{7} {(3 i - 2)}^{2}$
81628	Find the Inflection Points	f(x)=1/4x^4+5x^3+75/2x^2	$f (x) = \frac{1}{4} x^{4} + 5 x^{3} + \frac{75}{2} x^{2}$
81629	Find dx/dy	y=(x^2+5)(3x+1)	$y = (x^{2} + 5) (3 x + 1)$
81630	Find the Antiderivative	(e^x)/(e^x+2)	$\frac{e^{x}}{e^{x} + 2}$
81631	Find the Derivative - d/dx	((x-3)^3)/(x^2)	$\frac{{(x - 3)}^{3}}{x^{2}}$
81632	Find the Derivative - d/dx	natural log of \|x^2-1\|	$\ln (\| x^{2} - 1 \|)$
81633	Find the Derivative - d/dx	(arcsin(e^(3x)))	$(\arcsin (e^{3 x}))$
81634	Find the Maximum/Minimum Value	g(x)=xe^(3x)	$g (x) = x e^{3 x}$
81635	Evaluate the Integral	integral from 0 to infinity of 2xe^(x^2) with respect to x	$\int_{0}^{\infty} 2 x e^{x^{2}} d x$
81636	Find the Skew	2 , 8 , 8 , 12	$2$ , $8$ , $8$ , $12$
81637	Find the Derivative - d/dx	x^2* natural log of x	$x^{2} \cdot \ln (x)$
81638	Evaluate the Summation	sum from i=6 to 23 of i^2-2i+7	$\sum_{i = 6}^{23} i^{2} - 2 i + 7$
81639	Find the Antiderivative	natural log of 1+x	$\ln (1 + x)$
81640	Find the Antiderivative	(12x^2-4x)dx	$(12 x^{2} - 4 x) d x$
81641	Evaluate the Limit	limit as x approaches 2 from the left of (1x^2-2x)/(x^2-x-2)	$lim_{x \to 2^{-}} \frac{1 x^{2} - 2 x}{x^{2} - x - 2}$
81642	Evaluate the Integral	integral from 0 to pi/3 of sin(x)cos(x)^3 with respect to x	$\int_{0}^{\frac{π}{3}} \sin (x) \cos^{3} (x) d x$
81643	Evaluate the Limit	limit as x approaches negative infinity of (4x^3+3x^2)/(x-7x^2)	$lim_{x \to - \infty} \frac{4 x^{3} + 3 x^{2}}{x - 7 x^{2}}$
81644	Evaluate the Limit	limit as x approaches 0 of (e^x-cos(x)-2x)/(x^2-2x)	$lim_{x \to 0} \frac{e^{x} - \cos (x) - 2 x}{x^{2} - 2 x}$
81645	Evaluate the Limit	limit as x approaches 0 of (x+e^(2x))^(1/x)	$lim_{x \to 0} {(x + e^{2 x})}^{\frac{1}{x}}$
81646	Evaluate the Integral	integral of (2x+1)(2x-1) with respect to x	$\int (2 x + 1) (2 x - 1) d x$
81647	Find the Maximum/Minimum Value	-x(x+2)(x-2)	$- x (x + 2) (x - 2)$
81648	Find the Derivative - d/dx	2x-pi	$2 x - π$
81649	Evaluate the Integral	integral of x^(3/4)+x^(4/3) with respect to x	$\int x^{\frac{3}{4}} + x^{\frac{4}{3}} d x$
81650	Integrate By Parts	integral from 0 to 1 of xe^x with respect to x	$\int_{0}^{1} x e^{x} d x$
81651	Find dy/dx	3y^2-y=-2x^2	$3 y^{2} - y = - 2 x^{2}$
81652	Evaluate the Integral	integral of ( cube root of x+cos(2x+5)) with respect to x	$\int (\sqrt[3]{x} + \cos (2 x + 5)) d x$
81653	Find the Antiderivative	(2x+1)/(x^2+x+1)	$\frac{2 x + 1}{x^{2} + x + 1}$
81654	Find dy/dx	4xy-x^2-2=2y^2	$4 x y - x^{2} - 2 = 2 y^{2}$
81655	Evaluate the Integral	integral of 1/( square root of 8-2x-x^2) with respect to x	$\int \frac{1}{\sqrt{8 - 2 x - x^{2}}} d x$
81656	Find the Derivative - d/dx	(darccot(3x))/(dx)	$\frac{d arccot (3 x)}{d x}$
81657	Evaluate the Limit	limit as x approaches 0 of x^2+3x-2+(2x)/(x-1)	$lim_{x \to 0} x^{2} + 3 x - 2 + \frac{2 x}{x - 1}$
81658	Find dy/dx	2=5xy+5y	$2 = 5 x y + 5 y$
81659	Evaluate the Integral	integral from -1/3 to 1/3 of 1/(1+9x^2) with respect to x	$\int_{- \frac{1}{3}}^{\frac{1}{3}} \frac{1}{1 + 9 x^{2}} d x$
81660	Find dy/dx	2y^2-xy-5+x^3=0	$2 y^{2} - x y - 5 + x^{3} = 0$
81661	Find dy/dx	-2y^2+x^2=-2+y+2y^3	$- 2 y^{2} + x^{2} = - 2 + y + 2 y^{3}$
81662	Evaluate the Integral	integral from 0 to 3 of (1/2x-1) with respect to x	$\int_{0}^{3} (\frac{1}{2} x - 1) d x$
81663	Integrate Using u-Substitution	integral of cos(2x) with respect to x	$\int \cos (2 x) d x$
81664	Determine if Continuous	f(x)=(2x^2+5x-3)/(x+3)	$f (x) = \frac{2 x^{2} + 5 x - 3}{x + 3}$
81665	Find the Second Derivative	y = fifth root of x/(x^2-1)	$y = \sqrt[5]{\frac{x}{x^{2} - 1}}$
81666	Find the Third Derivative	y=x^5-2/(x^3)-4x+2	$y = x^{5} - \frac{2}{x^{3}} - 4 x + 2$
81667	Find the Derivative - d/dx	d/(dx)(arctan(3x))	$\frac{d}{d x} (\arctan (3 x))$
81668	Evaluate the Integral	integral from 0 to 6 of (x^2+x+1) with respect to x	$\int_{0}^{6} (x^{2} + x + 1) d x$
81669	Find the Antiderivative	1+x	$1 + x$
81670	Find the Derivative - d/dx	3e^(x/3)	$3 e^{\frac{x}{3}}$
81671	Find the Percentage Rate of Change	f(t)=1500(1.074)^t	$f (t) = 1500 {(1.074)}^{t}$
81672	Find the Antiderivative	5-3(1+x^2)^-1	$5 - 3 {(1 + x^{2})}^{- 1}$
81673	Find the Skew	2 , 6 , 7 , 8 , 18	$2$ , $6$ , $7$ , $8$ , $18$
81674	Find the Derivative - d/dx	x/2+2/x	$\frac{x}{2} + \frac{2}{x}$
81675	Evaluate the Limit	limit as z approaches 2 of ((2z+z^2)/(z^2+4))^3	$lim_{z \to 2} {(\frac{2 z + z^{2}}{z^{2} + 4})}^{3}$
81676	Find the Derivative - d/dx	x^2y+xy^2=3x	$x^{2} y + x y^{2} = 3 x$
81677	Find the Antiderivative	f(x)=4/(5x-2)+7	$f (x) = \frac{4}{5 x - 2} + 7$
81678	Find the Concavity	f(x)=3/20x^5-7x^3	$f (x) = \frac{3}{20} x^{5} - 7 x^{3}$
81679	Evaluate the Limit	limit as x approaches 3 of 6/(x^2-9)-1/(x-3)	$lim_{x \to 3} \frac{6}{x^{2} - 9} - \frac{1}{x - 3}$
81680	Evaluate the Integral	integral of (t^2-cos(t)) with respect to t	$\int (t^{2} - \cos (t)) d t$
81681	Find the Antiderivative	f(x)=x^2+2x-1	$f (x) = x^{2} + 2 x - 1$
81682	Find dy/dx	-2y^2+2x^2=-3x^3+y	$- 2 y^{2} + 2 x^{2} = - 3 x^{3} + y$
81683	Evaluate the Limit	limit as x approaches 0 of (3/(x+3)-3/3)/(3x)	$lim_{x \to 0} \frac{\frac{3}{x + 3} - \frac{3}{3}}{3 x}$
81684	Find the Derivative - d/dx	x^5e^(-3 natural log of x)	$x^{5} e^{- 3 \ln (x)}$
81685	Find dy/dx	-2x^3+y^3+x=5	$- 2 x^{3} + y^{3} + x = 5$
81686	Find dy/dx	y=((x+1)/(x-1))^3	$y = {(\frac{x + 1}{x - 1})}^{3}$
81687	Evaluate the Integral	integral of 1/(theta^2)cos(1/theta) with respect to theta	$\int \frac{1}{θ^{2}} \cos (\frac{1}{θ}) d θ$
81688	Find dy/dx	-x^3+5x-3y^2+2=0	$- x^{3} + 5 x - 3 y^{2} + 2 = 0$
81689	Find the Antiderivative	f(x)=(x^4+2)/(x^2)	$f (x) = \frac{x^{4} + 2}{x^{2}}$
81690	Solve the Differential Equation	xy'-2y=2	$x y' - 2 y = 2$
81691	Find Where Increasing/Decreasing	f(x)=5/2x^-4	$f (x) = \frac{5}{2} x^{- 4}$
81692	Find the Antiderivative	5+x+x^2+x^3	$5 + x + x^{2} + x^{3}$
81693	Evaluate the Limit	limit as x approaches pi of (sin(x))/(tan(x))	$lim_{x \to π} \frac{\sin (x)}{\tan (x)}$
81694	Integrate Using u-Substitution	integral from -6 to 0 of \|x^3+27\| with respect to x	$\int_{- 6}^{0} \| x^{3} + 27 \| d x$
81695	Evaluate the Integral	integral of tgx with respect to x	$\int t g x d x$
81696	Evaluate Using L'Hospital's Rule	limit as t approaches 0 of (sin(t))/( natural log of 2e^t-1)	$lim_{t \to 0} \frac{\sin (t)}{\ln (2 e^{t} - 1)}$
81697	Find the Second Derivative	e^x+100e+8x^4+49	$e^{x} + 100 e + 8 x^{4} + 49$
81698	Evaluate the Integral	integral from 0 to a^(2/5) of x^4 square root of a^2-x^5 with respect to x	$\int_{0}^{a^{\frac{2}{5}}} x^{4} \sqrt{a^{2} - x^{5}} d x$
81699	Evaluate the Limit	limit as x approaches 0 of ((x^2-4)^2-16)/(x^2)	$lim_{x \to 0} \frac{{(x^{2} - 4)}^{2} - 16}{x^{2}}$
81700	Evaluate Using L'Hospital's Rule	limit as x approaches 2 of (cos(4-2x)-1)/( natural log of 2x-3)	$lim_{x \to 2} \frac{\cos (4 - 2 x) - 1}{\ln (2 x - 3)}$