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Popular Calculus Problems

integral of 1/(sqrt(x)(x+\sqrt{x))}	\int\:\frac{1}{\sqrt{x}(x+\sqrt{x})}dx
integral of (3x-1)(sqrt(x)+1)	\int\:(3x-1)(\sqrt{x}+1)dx
integral of (sin(3x))/(sqrt(2+cos(3x)))	\int\:\frac{\sin(3x)}{\sqrt{2+\cos(3x)}}dx
integral of arcos(x)	\int\:ar\cos(x)dx
derivative of y=xsqrt((a^2-x^2)/x)	derivative\:y=x\sqrt{\frac{a^{2}-x^{2}}{x}}
area x=y^2-12,x=4y	area\:x=y^{2}-12,x=4y
integral of cos(y)e^{5sin(y)}	\int\:\cos(y)e^{5\sin(y)}dy
sum from n=0 to infinity of (1^n)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{1^{n}}{n!}
integral of (5+x^3)(4-x^2)	\int\:(5+x^{3})(4-x^{2})dx
integral of (x^{3/2}+7)^6sqrt(x)	\int\:(x^{\frac{3}{2}}+7)^{6}\sqrt{x}dx
limit as x approaches 5 of 2	\lim\:_{x\to\:5}(2)
tangent of x^2-x^4	tangent\:x^{2}-x^{4}
integral of e^{-6x^2}	\int\:e^{-6x^{2}}dx
integral of ((ln(x))/x)	\int\:(\frac{\ln(x)}{x})dx
limit as x approaches infinity of 6x^4	\lim\:_{x\to\:\infty\:}(6x^{4})
tangent of y=2x(x+1)^2,(0,0)	tangent\:y=2x(x+1)^{2},(0,0)
integral of 3x^2+6x+5	\int\:3x^{2}+6x+5dx
(\partial)/(\partial y)(z^3-x^2y)	\frac{\partial\:}{\partial\:y}(z^{3}-x^{2}y)
(xcos(x))^'	(x\cos(x))^{\prime\:}
derivative of f(x)=x^3(3-x^2)	derivative\:f(x)=x^{3}(3-x^{2})
derivative of f(x)= x/(x^2-7)	derivative\:f(x)=\frac{x}{x^{2}-7}
integral of (2x)/((x-3)^2)	\int\:\frac{2x}{(x-3)^{2}}dx
limit as n approaches 2 of 1/(n^2)	\lim\:_{n\to\:2}(\frac{1}{n^{2}})
limit as x approaches 2+of sqrt(x^2-4)	\lim\:_{x\to\:2+}(\sqrt{x^{2}-4})
derivative of (3x^2+x+3(x-2)(3x))	\frac{d}{dx}((3x^{2}+x+3)(x-2)(3x))
derivative of 6x^2+5x	\frac{d}{dx}(6x^{2}+5x)
4y^{''}-4y^'+26y=0	4y^{\prime\:\prime\:}-4y^{\prime\:}+26y=0
maclaurin ln(x+1)	maclaurin\:\ln(x+1)
integral of (4x)/(2+2x^2)	\int\:\frac{4x}{2+2x^{2}}dx
integral of (ln(6x))/x	\int\:\frac{\ln(6x)}{x}dx
integral of (sqrt(cos(2x))-sin(2x))^2	\int\:(\sqrt{\cos(2x)}-\sin(2x))^{2}dx
derivative of (4x^3-6(4x^2+4))	\frac{d}{dx}((4x^{3}-6)(4x^{2}+4))
integral of 1/(sqrt((1-x^2)^3))	\int\:\frac{1}{\sqrt{(1-x^{2})^{3}}}dx
derivative of (ln(x)/(9x))	\frac{d}{dx}(\frac{\ln(x)}{9x})
integral of (1/(e^{3t)})	\int\:(\frac{1}{e^{3t}})dt
limit as x approaches 0 of (e-1)/x	\lim\:_{x\to\:0}(\frac{e-1}{x})
derivative of x^4-3x^2+3	\frac{d}{dx}(x^{4}-3x^{2}+3)
limit as x approaches 1 of (\|3-x\|)/(3-x)	\lim\:_{x\to\:1}(\frac{\left\|3-x\right\|}{3-x})
derivative of (x^2/(5+x))	\frac{d}{dx}(\frac{x^{2}}{5+x})
derivative of e^{-t}	derivative\:e^{-t}
limit as x approaches 7 of 9x+\|x-7\|	\lim\:_{x\to\:7}(9x+\left\|x-7\right\|)
y^'-ay=0	y^{\prime\:}-ay=0
y^{''}+6y^'+9y=3e^{-3t}	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=3e^{-3t}
(dy)/(dx)+y/x =1	\frac{dy}{dx}+\frac{y}{x}=1
limit as x approaches 2 of 3pi	\lim\:_{x\to\:2}(3π)
inverse oflaplace 1/(s*(s+1))	inverselaplace\:\frac{1}{s\cdot\:(s+1)}
sum from n=1 to infinity of (n+4)/(n^2)	\sum\:_{n=1}^{\infty\:}\frac{n+4}{n^{2}}
y^{''}+16y=0	y^{\prime\:\prime\:}+16y=0
derivative of (0.25/(\sqrt[5]{x^2)})	\frac{d}{dx}(\frac{0.25}{\sqrt[5]{x^{2}}})
(\partial)/(\partial x)((x^{1/2}+y^{1/2})^2)	\frac{\partial\:}{\partial\:x}((x^{\frac{1}{2}}+y^{\frac{1}{2}})^{2})
integral of 5+(3x^2)/(sqrt(2x^3+7))	\int\:5+\frac{3x^{2}}{\sqrt{2x^{3}+7}}dx
integral of 300te^{(-t^2)/7}	\int\:300te^{\frac{-t^{2}}{7}}dt
limit as x approaches 0 of (cos(5x))/x	\lim\:_{x\to\:0}(\frac{\cos(5x)}{x})
(\partial)/(\partial x)(6x^2+y^2-7y)	\frac{\partial\:}{\partial\:x}(6x^{2}+y^{2}-7y)
inverse oflaplace e^{-6s}	inverselaplace\:e^{-6s}
(\partial)/(\partial x)(56ye^{8x})	\frac{\partial\:}{\partial\:x}(56ye^{8x})
integral of (8+x)(2x-8)	\int\:(8+x)(2x-8)dx
(ln(x+sqrt(1+x^2)))^'	(\ln(x+\sqrt{1+x^{2}}))^{\prime\:}
integral of ((y+1))/y	\int\:\frac{(y+1)}{y}dy
derivative of f(x)=(e^x)/(x^2+6)	derivative\:f(x)=\frac{e^{x}}{x^{2}+6}
derivative of (sin(t)/(sqrt(1+x^2)))	\frac{d}{dx}(\frac{\sin(t)}{\sqrt{1+x^{2}}})
integral of x^3e^{ax^4}	\int\:x^{3}e^{ax^{4}}dx
integral of (2(x^2+1))/(x(x^2+2))	\int\:\frac{2(x^{2}+1)}{x(x^{2}+2)}dx
limit as x approaches 4-of 1/(x^2-16)	\lim\:_{x\to\:4-}(\frac{1}{x^{2}-16})
integral of x/(sqrt((1-x^2)))	\int\:\frac{x}{\sqrt{(1-x^{2})}}dx
tangent of y=ln(x^2-4x+1),(4,0)	tangent\:y=\ln(x^{2}-4x+1),(4,0)
derivative of 1/(2sqrt(x+8))	derivative\:\frac{1}{2\sqrt{x+8}}
derivative of x^{5cos(x})	\frac{d}{dx}(x^{5\cos(x)})
limit as x approaches pi/4 of (tan(4x))/(4x-pi)	\lim\:_{x\to\:\frac{π}{4}}(\frac{\tan(4x)}{4x-π})
integral of 3x^2(x^3-5)^7	\int\:3x^{2}(x^{3}-5)^{7}dx
integral of 28(7x-2)^3	\int\:28(7x-2)^{3}dx
integral from-1 to 3 of-2x^2+4x+6	\int\:_{-1}^{3}-2x^{2}+4x+6dx
integral of (cos(x))/(1-cos^2(x))	\int\:\frac{\cos(x)}{1-\cos^{2}(x)}dx
-y^{'''}-y^{''}+5y^{''}-3=0	-y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+5y^{\prime\:\prime\:}-3=0
(\partial)/(\partial x)(sqrt(17-4x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{17-4x^{2}-y^{2}})
(\partial)/(\partial x)(y/(cos(x)))	\frac{\partial\:}{\partial\:x}(\frac{y}{\cos(x)})
derivative of 4/5 ln((9x^2-6^7))	\frac{d}{dx}(\frac{4}{5}\ln((9x^{2}-6)^{7}))
integral from 2 to 4 of ((2x-3))/6	\int\:_{2}^{4}\frac{(2x-3)}{6}dx
limit as x approaches 2 of x^2-x	\lim\:_{x\to\:2}(x^{2}-x)
limit as x approaches infinity of (7^{12}-2176782336)/(7^{11)}	\lim\:_{x\to\:\infty\:}(\frac{7^{12}-2176782336}{7^{11}})
integral of (x^2)/((1-4x^2)^{3/2)}	\int\:\frac{x^{2}}{(1-4x^{2})^{\frac{3}{2}}}dx
integral from 0 to 1 of e^{2x}-e^x	\int\:_{0}^{1}e^{2x}-e^{x}dx
integral of (3x+1)^4	\int\:(3x+1)^{4}dx
d/(da)(sin(2a)+sin(a))	\frac{d}{da}(\sin(2a)+\sin(a))
integral of 5ln(\sqrt[3]{x})	\int\:5\ln(\sqrt[3]{x})dx
integral from 0 to pi/2 of 4sqrt(2)	\int\:_{0}^{\frac{π}{2}}4\sqrt{2}
derivative of 4e^{arccos(4x)}	derivative\:4e^{\arccos(4x)}
integral of 3x^3	\int\:3x^{3}dx
tangent of f(x)=ln(x^2-2x+1),\at x=2	tangent\:f(x)=\ln(x^{2}-2x+1),\at\:x=2
y^{'''}-y^{''}+y^'-y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+y^{\prime\:}-y=0
derivative of g(x)=sqrt(7-x)	derivative\:g(x)=\sqrt{7-x}
limit as x approaches 4 of 3	\lim\:_{x\to\:4}(3)
(2r-1)/t dr+(r-2r^2)/(t^2-1)dt=0,r(2)=4	\frac{2r-1}{t}dr+\frac{r-2r^{2}}{t^{2}-1}dt=0,r(2)=4
(\partial)/(\partial r)(1/(r^2))	\frac{\partial\:}{\partial\:r}(\frac{1}{r^{2}})
derivative of (128/((1+4x)^3))	\frac{d}{dx}(\frac{128}{(1+4x)^{3}})
derivative of sqrt(x)+6\sqrt[3]{x}	\frac{d}{dx}(\sqrt{x}+6\sqrt[3]{x})
d/(dt)(te^{-3t})	\frac{d}{dt}(te^{-3t})
derivative of (6(x^2+1)/((x^2-3)^3))	\frac{d}{dx}(\frac{6(x^{2}+1)}{(x^{2}-3)^{3}})
area e^x,xe^{x^2},0,1	area\:e^{x},xe^{x^{2}},0,1
inverse oflaplace (2s+5)/(s^2+6s+34)	inverselaplace\:\frac{2s+5}{s^{2}+6s+34}

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