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Popular Calculus Problems

integral from 0 to 1/2 of arcsin(x)	\int\:_{0}^{\frac{1}{2}}\arcsin(x)dx
integral of (e^{-x})/(x^3)	\int\:\frac{e^{-x}}{x^{3}}dx
integral of 9tan^3(2x)sec^5(2x)	\int\:9\tan^{3}(2x)\sec^{5}(2x)dx
integral from-5 to 5 of sqrt(1+x^2)	\int\:_{-5}^{5}\sqrt{1+x^{2}}dx
(e^y)^'	(e^{y})^{\prime\:}
integral of 1/((x^2-36)^{3/2)}	\int\:\frac{1}{(x^{2}-36)^{\frac{3}{2}}}dx
integral of (1-x^2)/2	\int\:\frac{1-x^{2}}{2}dx
derivative of csc^2(x)-5	derivative\:\csc^{2}(x)-5
inverse oflaplace (s-4)/(2s^2+s+8)	inverselaplace\:\frac{s-4}{2s^{2}+s+8}
(\partial)/(\partial y)(3x^2+5y^2)	\frac{\partial\:}{\partial\:y}(3x^{2}+5y^{2})
xy^'+y=-2xy^2,y(1)=7	xy^{\prime\:}+y=-2xy^{2},y(1)=7
derivative of log_{2}(x-1-2)	\frac{d}{dx}(\log_{2}(x-1)-2)
derivative of y=x^2e^x-2xe^x+6e^x	derivative\:y=x^{2}e^{x}-2xe^{x}+6e^{x}
tangent of f(x)=16sqrt(x),\at x=16	tangent\:f(x)=16\sqrt{x},\at\:x=16
simplify (2x^{-2}+3)^{-3}	simplify\:(2x^{-2}+3)^{-3}
integral of 1/(10^5x-x^2)	\int\:\frac{1}{10^{5}x-x^{2}}dx
integral of 4x^{1/3}+2x^{-1/3}	\int\:4x^{\frac{1}{3}}+2x^{-\frac{1}{3}}dx
y^'=y(xy^6+3)	y^{\prime\:}=y(xy^{6}+3)
2x^{''}+40x=0	2x^{\prime\:\prime\:}+40x=0
derivative of (sqrt(x)-5)/(sqrt(x)+5)	derivative\:\frac{\sqrt{x}-5}{\sqrt{x}+5}
laplacetransform f(t)=(1+e^{2t})^2	laplacetransform\:f(t)=(1+e^{2t})^{2}
derivative of 4-6x	\frac{d}{dx}(4-6x)
derivative of sqrt(x)-9	\frac{d}{dx}(\sqrt{x}-9)
integral of 14arctan(sqrt(x))	\int\:14\arctan(\sqrt{x})dx
(dx)/(dt)+tx^3+x/t =0	\frac{dx}{dt}+tx^{3}+\frac{x}{t}=0
integral of 1/(3\sqrt[3]{x^5)}	\int\:\frac{1}{3\sqrt[3]{x^{5}}}dx
integral from t-1 to 2 of-t+2	\int\:_{t-1}^{2}-t+2dt
derivative of f(x)=(2x+3)^3	derivative\:f(x)=(2x+3)^{3}
derivative of 1+3x	\frac{d}{dx}(1+3x)
integral from 1 to 4 of t^4ln(3t)	\int\:_{1}^{4}t^{4}\ln(3t)dt
integral of (x^2-2x+1)e^{2x}	\int\:(x^{2}-2x+1)e^{2x}dx
(\partial)/(\partial x)(2xy-cos(x+y)-e^y)	\frac{\partial\:}{\partial\:x}(2xy-\cos(x+y)-e^{y})
sum from n=5 to infinity of ln(n)-ln(2n)	\sum\:_{n=5}^{\infty\:}\ln(n)-\ln(2n)
derivative of-(cos(x)ln(sec(x)+tan(x)))	\frac{d}{dx}(-(\cos(x))\ln(\sec(x)+\tan(x)))
limit as x approaches pi of 2cot(x)	\lim\:_{x\to\:π}(2\cot(x))
integral of e^{t^3}	\int\:e^{t^{3}}dt
integral of r^2(r^3+5)^8	\int\:r^{2}(r^{3}+5)^{8}dr
integral of 7cos(sqrt(4x))	\int\:7\cos(\sqrt{4x})dx
f(x)=3x^4-7ln(x)	f(x)=3x^{4}-7\ln(x)
integral of 2\sqrt[3]{x}	\int\:2\sqrt[3]{x}dx
integral of sin^3(2x)cot(2x)	\int\:\sin^{3}(2x)\cot(2x)dx
(\partial)/(\partial y)(y^2+x)	\frac{\partial\:}{\partial\:y}(y^{2}+x)
inverse oflaplace 1/s-s/(s^2+1)	inverselaplace\:\frac{1}{s}-\frac{s}{s^{2}+1}
integral of 1/(2sqrt(3-x)\sqrt{x+1)}	\int\:\frac{1}{2\sqrt{3-x}\sqrt{x+1}}dx
derivative of ln(x^2e^x)	\frac{d}{dx}(\ln(x^{2}e^{x}))
sum from n=0 to infinity of 1/((n^3-n))	\sum\:_{n=0}^{\infty\:}\frac{1}{(n^{3}-n)}
y^'+8x-1y=x^8,y(1)=9	y^{\prime\:}+8x-1y=x^{8},y(1)=9
derivative of psqrt(p)	derivative\:p\sqrt{p}
integral of ((3x+1)^2)/(244)	\int\:\frac{(3x+1)^{2}}{244}dx
d/(dθ)(sin(θ)+θcos(θ))	\frac{d}{dθ}(\sin(θ)+θ\cos(θ))
(\partial)/(\partial x)(2sin(3x+2y))	\frac{\partial\:}{\partial\:x}(2\sin(3x+2y))
integral of (sqrt(y+1))/y	\int\:\frac{\sqrt{y+1}}{y}dy
derivative of e^xcos(x^2)	\frac{d}{dx}(e^{x}\cos(x^{2}))
limit as y approaches-1 of-y^5-3y^4	\lim\:_{y\to\:-1}(-y^{5}-3y^{4})
tangent of f(x)=e^{2x},(0,1)	tangent\:f(x)=e^{2x},(0,1)
sum from n=1 to infinity of (-1)^nn^{-1}	\sum\:_{n=1}^{\infty\:}(-1)^{n}n^{-1}
y^{''}+5y^'=e^{-t},y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}+5y^{\prime\:}=e^{-t},y(0)=0,y^{\prime\:}(0)=0
y^'=8x+y,y(0)=6	y^{\prime\:}=8x+y,y(0)=6
(\partial)/(\partial z)(e^x+yz)	\frac{\partial\:}{\partial\:z}(e^{x}+yz)
simplify sqrt(f(x))	simplify\:\sqrt{f(x)}
limit as x approaches 6+of x/(36-x^2)	\lim\:_{x\to\:6+}(\frac{x}{36-x^{2}})
derivative of 2xarcsin(x)	\frac{d}{dx}(2x\arcsin(x))
limit as x approaches 2 of [x]	\lim\:_{x\to\:2}([x])
derivative of (2x^3+x^2-2x/(x^4-2x^2-4))	\frac{d}{dx}(\frac{2x^{3}+x^{2}-2x}{x^{4}-2x^{2}-4})
tangent of y=6x-x^2(1.5)	tangent\:y=6x-x^{2}(1.5)
derivative of x^2log_{e}(2x)	\frac{d}{dx}(x^{2}\log_{e}(2x))
(dy)/(dx)+4tan(4x)y=3cos(4x)	\frac{dy}{dx}+4\tan(4x)y=3\cos(4x)
slope of (0,1),(4,-5)	slope\:(0,1),(4,-5)
derivative of (1+x^2)/((1-x^2)^2)	derivative\:\frac{1+x^{2}}{(1-x^{2})^{2}}
derivative of ln(4-x)	\frac{d}{dx}(\ln(4-x))
derivative of (2-x/(x+4))	\frac{d}{dx}(\frac{2-x}{x+4})
derivative of f(t)=5t-8t^2	derivative\:f(t)=5t-8t^{2}
(\partial)/(\partial y)(-xy^2z+4xy)	\frac{\partial\:}{\partial\:y}(-xy^{2}z+4xy)
(\partial)/(\partial x)(sin(x+y)+(x+y))	\frac{\partial\:}{\partial\:x}(\sin(x+y)+(x+y))
integral of 3/(x^3+x)	\int\:\frac{3}{x^{3}+x}dx
integral from 0 to 2 of te^{2t}	\int\:_{0}^{2}te^{2t}dt
(\partial)/(\partial x)(x^2e^{3xy})	\frac{\partial\:}{\partial\:x}(x^{2}e^{3xy})
integral of (x/(xsqrt(x^2+36)))	\int\:(\frac{x}{x\sqrt{x^{2}+36}})dx
(\partial)/(\partial y)(ln(x+y^2))	\frac{\partial\:}{\partial\:y}(\ln(x+y^{2}))
integral from 0 to 5 of 1/(x^{20/21)}	\int\:_{0}^{5}\frac{1}{x^{\frac{20}{21}}}dx
integral of tan(2x)sec^8(2x)	\int\:\tan(2x)\sec^{8}(2x)dx
integral of ((x^2-1))/(x^2)	\int\:\frac{(x^{2}-1)}{x^{2}}dx
integral of (e^{2x})/(e^{2x)+3e^x+2}	\int\:\frac{e^{2x}}{e^{2x}+3e^{x}+2}dx
(\partial)/(\partial x)(tan(ln(x-y)))	\frac{\partial\:}{\partial\:x}(\tan(\ln(x-y)))
(\partial)/(\partial x)((e^{xy})/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{e^{xy}}{x+y})
integral of (2picos(pix))	\int\:(2π\cos(πx))dx
integral of-sin(x)cos(x)	\int\:-\sin(x)\cos(x)dx
derivative of \sqrt[3]{(8x^2-3/(x^2+2)})	\frac{d}{dx}(\sqrt[3]{\frac{8x^{2}-3}{x^{2}+2}})
integral of (e^3)/x	\int\:\frac{e^{3}}{x}dx
limit as x approaches 0 of (\|x\|)/(4x)	\lim\:_{x\to\:0}(\frac{\left\|x\right\|}{4x})
(d^2y)/(dx^2)-12(dy)/(dx)+36y=0	\frac{d^{2}y}{dx^{2}}-12\frac{dy}{dx}+36y=0
integral from 0 to 4sqrt(2 of)2-x^{2/5}	\int\:_{0}^{4\sqrt{2}}2-x^{\frac{2}{5}}dx
integral of tan(t/2)	\int\:\tan(\frac{t}{2})dt
integral from 0 to 1 of (x+7)(x-8)	\int\:_{0}^{1}(x+7)(x-8)dx
limit as x approaches-4 of-x^2+2x-8	\lim\:_{x\to\:-4}(-x^{2}+2x-8)
derivative of 5(e^x)^{-4}	derivative\:5(e^{x})^{-4}
tangent of f(x)= 1/(x^6),(-3, 1/729)	tangent\:f(x)=\frac{1}{x^{6}},(-3,\frac{1}{729})
(\partial)/(\partial w)(ve^w)	\frac{\partial\:}{\partial\:w}(ve^{w})
derivative of (x+1/x ^{10})	\frac{d}{dx}((x+\frac{1}{x})^{10})
integral of 2sin(x)e^x	\int\:2\sin(x)e^{x}dx

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