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Popular Calculus Problems

sum from n=1 to infinity of 1/(n^pi)	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{π}}
integral of 4tan^2(θ)	\int\:4\tan^{2}(θ)dθ
(\partial)/(\partial x)(sin(3x^3y-5xy^3))	\frac{\partial\:}{\partial\:x}(\sin(3x^{3}y-5xy^{3}))
integral of cos^7(7-x)sin(7-x)	\int\:\cos^{7}(7-x)\sin(7-x)dx
derivative of (5t+e^t)(3-sqrt(t))	derivative\:(5t+e^{t})(3-\sqrt{t})
(x^2y^3-1/(1+9x^2))((dx)/(dy))+x^3y^2=0	(x^{2}y^{3}-\frac{1}{1+9x^{2}})(\frac{dx}{dy})+x^{3}y^{2}=0
integral of x^2sqrt(1+x^2)	\int\:x^{2}\sqrt{1+x^{2}}dx
(\partial)/(\partial x)(x^2sin(3t))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(3t))
derivative of arcsin(e^{2x})	derivative\:\arcsin(e^{2x})
t^2(dy)/(dt)+y=0,y(5)=-1,t>0	t^{2}\frac{dy}{dt}+y=0,y(5)=-1,t>0
limit as x approaches-10 of 1/((x+10)^4)	\lim\:_{x\to\:-10}(\frac{1}{(x+10)^{4}})
integral of sqrt(1+8x)	\int\:\sqrt{1+8x}dx
integral of artan(x)	\int\:ar\tan(x)dx
integral of e^{-x} 1/x	\int\:e^{-x}\frac{1}{x}dx
integral of 2cos^3(2x)	\int\:2\cos^{3}(2x)dx
derivative of sin(θ)+csc(θ)	derivative\:\sin(θ)+\csc(θ)
derivative of sqrt((a^2+x^2/(a^2-x^2)))	\frac{d}{dx}(\sqrt{\frac{a^{2}+x^{2}}{a^{2}-x^{2}}})
integral from-1 to 0 of 2-e^{-x}	\int\:_{-1}^{0}2-e^{-x}dx
tangent of x/(x^2+4)	tangent\:\frac{x}{x^{2}+4}
inverse oflaplace 1/(s^2+2s)	inverselaplace\:\frac{1}{s^{2}+2s}
limit as x approaches 0 of (3x+9)^x	\lim\:_{x\to\:0}((3x+9)^{x})
(dy)/(dx)=-8yx	\frac{dy}{dx}=-8yx
derivative of 2x^{1/2}+2x^{-4}-1	\frac{d}{dx}(2x^{\frac{1}{2}}+2x^{-4}-1)
integral of (-5x)/(x^2+3x+4)	\int\:\frac{-5x}{x^{2}+3x+4}dx
(\partial)/(\partial x)(xln(ycos(x)))	\frac{\partial\:}{\partial\:x}(x\ln(y\cos(x)))
derivative of x^4-10x^2+9	\frac{d}{dx}(x^{4}-10x^{2}+9)
derivative of e^{x-2y}	\frac{d}{dx}(e^{x-2y})
integral of (x+20)/(x^2+18x+85)	\int\:\frac{x+20}{x^{2}+18x+85}dx
integral of sin^2(2x)cos(x)	\int\:\sin^{2}(2x)\cos(x)dx
derivative of e^ycos(x)	\frac{d}{dx}(e^{y}\cos(x))
derivative of y=x^2-7	derivative\:y=x^{2}-7
integral of (8x^3)/((x^4+5))	\int\:\frac{8x^{3}}{(x^{4}+5)}dx
integral of (x^3)/(x^2+x-6)	\int\:\frac{x^{3}}{x^{2}+x-6}dx
derivative of 2/x-3/(x^2)	\frac{d}{dx}(\frac{2}{x}-\frac{3}{x^{2}})
area x^3,x^2	area\:x^{3},x^{2}
derivative of (x+cos(x)^{cot(x)})	\frac{d}{dx}((x+\cos(x))^{\cot(x)})
y^{''}-2y^'+y=te^t+4,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}-2y^{\prime\:}+y=te^{t}+4,y(0)=1,y^{\prime\:}(0)=1
derivative of f(x)=x^4(3-x)^3	derivative\:f(x)=x^{4}(3-x)^{3}
derivative of θcos(θ)+sin(θ)	derivative\:θ\cos(θ)+\sin(θ)
integral from 6 to 8 of (98)/((x-6)^3)	\int\:_{6}^{8}\frac{98}{(x-6)^{3}}dx
limit as x approaches 2 of-1.999+2	\lim\:_{x\to\:2}(-1.999+2)
tangent of f(x)=-x^2+4sqrt(x)	tangent\:f(x)=-x^{2}+4\sqrt{x}
integral of (10x-2)/(5x^2-2x)	\int\:\frac{10x-2}{5x^{2}-2x}dx
integral of ((1+sin(x)))/(cos^2(x))	\int\:\frac{(1+\sin(x))}{\cos^{2}(x)}dx
limit as x approaches 0-of csc(x)	\lim\:_{x\to\:0-}(\csc(x))
y^{''}-25y=0,y(2)=-2,y^'(-2)=2	y^{\prime\:\prime\:}-25y=0,y(2)=-2,y^{\prime\:}(-2)=2
y^'=ycos(t)	y^{\prime\:}=y\cos(t)
maclaurin xcos(4x)	maclaurin\:x\cos(4x)
derivative of (sqrt(s)-5)/(sqrt(s)+1)	derivative\:\frac{\sqrt{s}-5}{\sqrt{s}+1}
integral of t^2sin(5t)	\int\:t^{2}\sin(5t)dt
d/(dn)((1+i)^n+(1-i)^n)	\frac{d}{dn}((1+i)^{n}+(1-i)^{n})
derivative of 4/x-1/(x^3)	\frac{d}{dx}(\frac{4}{x}-\frac{1}{x^{3}})
integral from 1 to 3 of f(2x)	\int\:_{1}^{3}f(2x)dx
limit as t approaches 0 of ln(t+1)	\lim\:_{t\to\:0}(\ln(t+1))
y^{''}+6y^'+8y=cos(3t)	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=\cos(3t)
tangent of f(x)=5x^3+4x,\at x=-1	tangent\:f(x)=5x^{3}+4x,\at\:x=-1
(dx)/(dt)=1+t-x-tx	\frac{dx}{dt}=1+t-x-tx
integral of 2(2x+4)^5	\int\:2(2x+4)^{5}dx
derivative of 4^4	\frac{d}{dx}(4^{4})
derivative of f(x)=(4-x)(2/(x^2)-3)	derivative\:f(x)=(4-x)(\frac{2}{x^{2}}-3)
tangent of y=-e^{-x-2},(-3,-e)	tangent\:y=-e^{-x-2},(-3,-e)
(\partial)/(\partial v)(v)	\frac{\partial\:}{\partial\:v}(v)
derivative of sqrt(x)+y	\frac{d}{dx}(\sqrt{x}+y)
limit as x approaches 3 of (x^3-9x)/((x^2)-3x)	\lim\:_{x\to\:3}(\frac{x^{3}-9x}{(x^{2})-3x})
limit as x approaches 3/2 of x	\lim\:_{x\to\:\frac{3}{2}}(x)
integral of (18)/(18+e^x)	\int\:\frac{18}{18+e^{x}}dx
derivative of 3^{x^3}	derivative\:3^{x^{3}}
derivative of p(x)=(x-3)^3-(x-2)^2+31	derivative\:p(x)=(x-3)^{3}-(x-2)^{2}+31
integral from 1/2 to 1 of (x+4)/(x^2+x)	\int\:_{\frac{1}{2}}^{1}\frac{x+4}{x^{2}+x}dx
integral from 0 to 1 of integral of 1	\int\:_{0}^{1}\int\:1dxdy
limit as x approaches 4 of sqrt(x+2)	\lim\:_{x\to\:4}(\sqrt{x+2})
integral from 1 to 8 of pi(x-1)	\int\:_{1}^{8}π(x-1)dx
tangent of f(x)=3x^2+8x+4,\at x=-1	tangent\:f(x)=3x^{2}+8x+4,\at\:x=-1
limit as x approaches 0 of x^3+2x^2-x-2	\lim\:_{x\to\:0}(x^{3}+2x^{2}-x-2)
limit as x approaches 0-of (x+\|x\|)/x	\lim\:_{x\to\:0-}(\frac{x+\left\|x\right\|}{x})
derivative of 1/x+1/(x^2+1/(x^3))	\frac{d}{dx}(\frac{1}{x}+\frac{1}{x^{2}}+\frac{1}{x^{3}})
limit as x approaches 0 of (x-1)/(x^3+x)	\lim\:_{x\to\:0}(\frac{x-1}{x^{3}+x})
tangent of y=sin(5x)+cos(6x)	tangent\:y=\sin(5x)+\cos(6x)
integral of (sqrt(x^2))/x	\int\:\frac{\sqrt{x^{2}}}{x}dx
area y=-5/9 x+5,(4,11)	area\:y=-\frac{5}{9}x+5,(4,11)
(\partial)/(\partial x)(e^{1-xy})	\frac{\partial\:}{\partial\:x}(e^{1-xy})
derivative of 1/(x^{1/3)}	derivative\:\frac{1}{x^{\frac{1}{3}}}
inverse oflaplace t-1	inverselaplace\:t-1
(\partial}{\partial y}(sin(\frac{2y)/x))	\frac{\partial\:}{\partial\:y}(\sin(\frac{2y}{x}))
integral of x/(x^2-2x+1)	\int\:\frac{x}{x^{2}-2x+1}dx
integral from 0 to 3 of 2^x	\int\:_{0}^{3}2^{x}dx
sum from n=0 to infinity of (n^3)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{3}}{2^{n}}
integral of 1/(sin^2(a)x)	\int\:\frac{1}{\sin^{2}(a)x}dx
y^'=x^5+2x^4-x-2	y^{\prime\:}=x^{5}+2x^{4}-x-2
laplacetransform t^{1/2}	laplacetransform\:t^{\frac{1}{2}}
sum from n=1 to infinity of (5^n)/n	\sum\:_{n=1}^{\infty\:}\frac{5^{n}}{n}
y^{''}-8y^'+25y=5x^3e^{-x}-7e^{-x}	y^{\prime\:\prime\:}-8y^{\prime\:}+25y=5x^{3}e^{-x}-7e^{-x}
derivative of (3x^5+7/(x^3))	\frac{d}{dx}(\frac{3x^{5}+7}{x^{3}})
derivative of f(x)=e^{x^6}-x+1	derivative\:f(x)=e^{x^{6}}-x+1
integral of (6t^2*\sqrt[3]{t})	\int\:(6t^{2}\cdot\:\sqrt[3]{t})dt
(\partial)/(\partial y)(x-y^2)	\frac{\partial\:}{\partial\:y}(x-y^{2})
area y=-x^2+4,y=3x	area\:y=-x^{2}+4,y=3x
derivative of (3-x^2/(3+x^2))	\frac{d}{dx}(\frac{3-x^{2}}{3+x^{2}})
(dy)/(dx)=sqrt(6y)e^{x+9}	\frac{dy}{dx}=\sqrt{6y}e^{x+9}
limit as x approaches 0 of (1-1/x)^x	\lim\:_{x\to\:0}((1-\frac{1}{x})^{x})

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