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Popular Calculus Problems

integral of (e^y+1)^2e^{-y}	\int\:(e^{y}+1)^{2}e^{-y}dy
integral of (x^3)/(x^2+x-2)	\int\:\frac{x^{3}}{x^{2}+x-2}dx
integral of (x^4)/(x^5-2)	\int\:\frac{x^{4}}{x^{5}-2}dx
derivative of (e^{1/x}/(x^2))	\frac{d}{dx}(\frac{e^{\frac{1}{x}}}{x^{2}})
limit as x approaches infinity of 1-3/x	\lim\:_{x\to\:\infty\:}(1-\frac{3}{x})
d/(dy)(-xy)	\frac{d}{dy}(-xy)
(dy)/(dx)=(x^5)/(3y^2)	\frac{dy}{dx}=\frac{x^{5}}{3y^{2}}
derivative of (x/9 ^2+(y/4)^2)=1	\frac{d}{dx}((\frac{x}{9})^{2}+(\frac{y}{4})^{2})=1
area 4-x^2,x-2	area\:4-x^{2},x-2
integral of 1/(sqrt(9+2x))	\int\:\frac{1}{\sqrt{9+2x}}dx
integral of (x^2)/(\sqrt[3]{x)}	\int\:\frac{x^{2}}{\sqrt[3]{x}}dx
derivative of ln^2(2*2^x-1/(x^2))	\frac{d}{dx}(\ln^{2}(2)\cdot\:2^{x}-\frac{1}{x^{2}})
integral from 1 to 2 of (1/x-1/(x^2))	\int\:_{1}^{2}(\frac{1}{x}-\frac{1}{x^{2}})dx
d/(dy)(4y^3-5y^3cos(y)+2y^5sin(y))	\frac{d}{dy}(4y^{3}-5y^{3}\cos(y)+2y^{5}\sin(y))
integral of (4x+2)sin(x^2+x+2)	\int\:(4x+2)\sin(x^{2}+x+2)dx
derivative of arcsin(7x^5)	\frac{d}{dx}(\arcsin(7x^{5}))
derivative of f(x)=sqrt(3x+x^2)	derivative\:f(x)=\sqrt{3x+x^{2}}
integral of x^{1/3}(x^{4/3}+9)^8	\int\:x^{\frac{1}{3}}(x^{\frac{4}{3}}+9)^{8}dx
integral of sin^2(2x)cos^5(2x)	\int\:\sin^{2}(2x)\cos^{5}(2x)dx
derivative of 1/(s^2+1)	derivative\:\frac{1}{s^{2}+1}
join 1/3 cot(9x)	join\:\frac{1}{3}\cot(9x)
limit as x approaches-2-of f(x)	\lim\:_{x\to\:-2-}(f(x))
derivative of (2x^2-9^{-1})	\frac{d}{dx}((2x^{2}-9)^{-1})
derivative of 3x^2-5x+2	\frac{d}{dx}(3x^{2}-5x+2)
derivative of 4/(t^2)-2/t	derivative\:\frac{4}{t^{2}}-\frac{2}{t}
tangent of f(x)=x^4,\at x=7	tangent\:f(x)=x^{4},\at\:x=7
integral of (e^{2x})/(1+e^x)	\int\:\frac{e^{2x}}{1+e^{x}}dx
derivative of ((x^2+32x^{1/2})/8)	\frac{d}{dx}(\frac{(x^{2}+32x^{\frac{1}{2}})}{8})
(e^y+1)^2e^{-y}dx+(e^x+1)e^{-x}dy=0	(e^{y}+1)^{2}e^{-y}dx+(e^{x}+1)e^{-x}dy=0
taylor 1/((x-1)^2)	taylor\:\frac{1}{(x-1)^{2}}
limit as x approaches 1 of (2-1)/(x^3-3)	\lim\:_{x\to\:1}(\frac{2-1}{x^{3}-3})
derivative of (x^3)/(3-x^2)	derivative\:\frac{x^{3}}{3-x^{2}}
integral from-9 to 0 of 1/((x-9)^2)	\int\:_{-9}^{0}\frac{1}{(x-9)^{2}}dx
integral of e^{sqrt(1-2x)}	\int\:e^{\sqrt{1-2x}}dx
integral of e^xsqrt(17+e^x)	\int\:e^{x}\sqrt{17+e^{x}}dx
sum from n=1 to infinity of tan(n)	\sum\:_{n=1}^{\infty\:}\tan(n)
limit as x approaches-3+of 2x^2+4x+3	\lim\:_{x\to\:-3+}(2x^{2}+4x+3)
integral of (x-6)/(x^2-6x+8)	\int\:\frac{x-6}{x^{2}-6x+8}dx
derivative of cos(1)	\frac{d}{dx}(\cos(1))
limit as x approaches 4 of 4/(x^{3/2)}	\lim\:_{x\to\:4}(\frac{4}{x^{\frac{3}{2}}})
limit as x approaches-3 of 2x^2+x^3+5x-2	\lim\:_{x\to\:-3}(2x^{2}+x^{3}+5x-2)
inverse oflaplace 6/s+821/(s^2+16)	inverselaplace\:\frac{6}{s}+8\cdot\:2\cdot\:\frac{1}{s^{2}+16}
integral of yze^{xz}	\int\:yze^{xz}dx
tangent of f(x)=(3x-5)(x+4),(2,6)	tangent\:f(x)=(3x-5)(x+4),(2,6)
integral from 3 to infinity of x/(x^2+1)	\int\:_{3}^{\infty\:}\frac{x}{x^{2}+1}dx
limit as x approaches-3 of (5x^2)/(x+3)	\lim\:_{x\to\:-3}(\frac{5x^{2}}{x+3})
(\partial)/(\partial y)(x+y^2)	\frac{\partial\:}{\partial\:y}(x+y^{2})
integral of 6x*csc^2(8x^2)	\int\:6x\cdot\:\csc^{2}(8x^{2})dx
limit as x approaches 0+of e^{(-1)/x}	\lim\:_{x\to\:0+}(e^{\frac{-1}{x}})
(\partial)/(\partial x)(x^2+y^2+z)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z)
limit as t approaches 1 of (3t-1)(5t^2+2)	\lim\:_{t\to\:1}((3t-1)(5t^{2}+2))
derivative of sin(xln(9x))	\frac{d}{dx}(\sin(x)\ln(9x))
(\partial)/(\partial x)(e^{sin^2(x)})	\frac{\partial\:}{\partial\:x}(e^{\sin^{2}(x)})
integral from 0 to 1 of 3^{3x}	\int\:_{0}^{1}3^{3x}dx
derivative of 1/(y^2)-5/(y^4)(y+9y^3)	derivative\:\frac{1}{y^{2}}-\frac{5}{y^{4}}(y+9y^{3})
(\partial)/(\partial x)(sin(xy^3))	\frac{\partial\:}{\partial\:x}(\sin(xy^{3}))
integral of x^3(5+x^4)^5	\int\:x^{3}(5+x^{4})^{5}dx
8(t+1)(dy)/(dt)-6y=12t	8(t+1)\frac{dy}{dt}-6y=12t
integral from 0 to 1 of (1+2^x)^22^{-x}	\int\:_{0}^{1}(1+2^{x})^{2}2^{-x}dx
(\partial)/(\partial x)(*e)	\frac{\partial\:}{\partial\:x}(\cdot\:e)
sum from n=1 to infinity of \sqrt[5]{(32)/(n^6)}	\sum\:_{n=1}^{\infty\:}\sqrt[5]{\frac{32}{n^{6}}}
derivative of f(x)=(x^2+1)(2-x)	derivative\:f(x)=(x^{2}+1)(2-x)
limit as x approaches-3 of sqrt(2x+5)	\lim\:_{x\to\:-3}(\sqrt{2x+5})
derivative of cos(x^{-6})	\frac{d}{dx}(\cos(x^{-6}))
tangent of f(x)=8e^x+x,\at x=0	tangent\:f(x)=8e^{x}+x,\at\:x=0
integral of (x+1)e^{3x+1}	\int\:(x+1)e^{3x+1}dx
integral of 5x^4-2x^5	\int\:5x^{4}-2x^{5}dx
inverse oflaplace 6s	inverselaplace\:6s
integral of 4cos(x^2)	\int\:4\cos(x^{2})dx
(tan(x)-sin(x)sin(y))dx+cos(x)cos(y)dy=0	(\tan(x)-\sin(x)\sin(y))dx+\cos(x)\cos(y)dy=0
xy^'-x-x^2-3y=0	xy^{\prime\:}-x-x^{2}-3y=0
integral of (3t^2)/(sqrt(t^3+5))	\int\:\frac{3t^{2}}{\sqrt{t^{3}+5}}dt
integral of x*sqrt(x+3)	\int\:x\cdot\:\sqrt{x+3}dx
(\partial)/(\partial y)(x+ysin(t))	\frac{\partial\:}{\partial\:y}(x+y\sin(t))
integral from 0 to pi of sin^2(xco)s^4x	\int\:_{0}^{π}\sin^{2}(xco)s^{4}xdx
integral of (sec^2(x)+2)	\int\:(\sec^{2}(x)+2)dx
limit as x approaches-7+of (x-4)/(x+7)	\lim\:_{x\to\:-7+}(\frac{x-4}{x+7})
(\partial)/(\partial x)(7+8xsqrt(y))	\frac{\partial\:}{\partial\:x}(7+8x\sqrt{y})
limit as x approaches 0 of 1/(sqrt(2x))	\lim\:_{x\to\:0}(\frac{1}{\sqrt{2x}})
derivative of 5x-e	\frac{d}{dx}(5x-e)
(\partial)/(\partial x)((6x-7y)/(y^2+x^2))	\frac{\partial\:}{\partial\:x}(\frac{6x-7y}{y^{2}+x^{2}})
xy^'=y+x^2sin(x),y(pi/6)=0	xy^{\prime\:}=y+x^{2}\sin(x),y(\frac{π}{6})=0
derivative of ((x^2+2/(x^3-1))^3)	\frac{d}{dx}((\frac{x^{2}+2}{x^{3}-1})^{3})
inverse oflaplace 1/(s^3(s^2+1))	inverselaplace\:\frac{1}{s^{3}(s^{2}+1)}
derivative of 3x^2ln(x+x^2)	\frac{d}{dx}(3x^{2}\ln(x)+x^{2})
integral of-1/(sin(y))	\int\:-\frac{1}{\sin(y)}dy
integral of e^{-21x}	\int\:e^{-21x}dx
integral of 1/(x^4-x^3)	\int\:\frac{1}{x^{4}-x^{3}}dx
laplacetransform cos(3x)	laplacetransform\:\cos(3x)
derivative of (10/(ln(x)))	\frac{d}{dx}(\frac{10}{\ln(x)})
t^2(dy)/(dt)+y=0,y(7)=-4	t^{2}\frac{dy}{dt}+y=0,y(7)=-4
integral of sin(2t)(cot(2t)+1)	\int\:\sin(2t)(\cot(2t)+1)dt
derivative of \|x-1\|^3	\frac{d}{dx}(\left\|x-1\right\|^{3})
limit as x approaches 0 of \|x-1\|	\lim\:_{x\to\:0}(\left\|x-1\right\|)
limit as x approaches 5 of 2xsqrt(5)	\lim\:_{x\to\:5}(2x\sqrt{5})
(\partial)/(\partial x)(e^{2x}*2)	\frac{\partial\:}{\partial\:x}(e^{2x}\cdot\:2)
derivative of f(x)=(2x-7)^4(x^2+x+1)^5	derivative\:f(x)=(2x-7)^{4}(x^{2}+x+1)^{5}
integral of (1+x^2)/(x^3)	\int\:\frac{1+x^{2}}{x^{3}}dx
(\partial)/(\partial x)(2-sqrt(y-x^2))	\frac{\partial\:}{\partial\:x}(2-\sqrt{y-x^{2}})
taylor cos(x/2)	taylor\:\cos(\frac{x}{2})

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