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Popular Calculus Problems

integral of sqrt(5x^2-4)	\int\:\sqrt{5x^{2}-4}dx
(d^2}{dx^2}(e^{\frac{-x^2)/2})	\frac{d^{2}}{dx^{2}}(e^{\frac{-x^{2}}{2}})
tangent of y=7x-6sqrt(x),(1,1)	tangent\:y=7x-6\sqrt{x},(1,1)
y^{''}+9y^'-10y=0	y^{\prime\:\prime\:}+9y^{\prime\:}-10y=0
(dy)/(dx)=2+sqrt(y-2x+3)	\frac{dy}{dx}=2+\sqrt{y-2x+3}
integral of (x^3)/((x^2+16)^3)	\int\:\frac{x^{3}}{(x^{2}+16)^{3}}dx
integral of (2x+7)/(x^2+2x+5)	\int\:\frac{2x+7}{x^{2}+2x+5}dx
(-xy^2-y)dx+(-x^2y-x)dy=0	(-xy^{2}-y)dx+(-x^{2}y-x)dy=0
integral from 0 to 4 of x^2-3x	\int\:_{0}^{4}x^{2}-3xdx
(\partial)/(\partial x)(15x^2+10y)	\frac{\partial\:}{\partial\:x}(15x^{2}+10y)
integral from 3 to 5 of (x^3)/8	\int\:_{3}^{5}\frac{x^{3}}{8}dx
integral from 0 to 2pi of sin(2x)sin(x)	\int\:_{0}^{2π}\sin(2x)\sin(x)dx
sum from n=0 to infinity of ((-1)/2)^n	\sum\:_{n=0}^{\infty\:}(\frac{-1}{2})^{n}
integral of x^5-5x^{-2}+2	\int\:x^{5}-5x^{-2}+2dx
tangent of f(x)=4x(x^2-4x+5)^9,\at x=2	tangent\:f(x)=4x(x^{2}-4x+5)^{9},\at\:x=2
derivative of 9e^{-4x}	\frac{d}{dx}(9e^{-4x})
y^3(dy)/(dx)+x^3=0	y^{3}\frac{dy}{dx}+x^{3}=0
(\partial)/(\partial y)(x^2-4xy-2y^2)	\frac{\partial\:}{\partial\:y}(x^{2}-4xy-2y^{2})
integral of (3x^2-6x+3)	\int\:(3x^{2}-6x+3)dx
integral from 0 to 1/4 of 5arcsin(4x)	\int\:_{0}^{\frac{1}{4}}5\arcsin(4x)dx
integral of (6x^3+5x^2-47x-36)/(x^2-9)	\int\:\frac{6x^{3}+5x^{2}-47x-36}{x^{2}-9}dx
taylor sqrt(10-x),1	taylor\:\sqrt{10-x},1
derivative of arccot(x/6)	derivative\:\arccot(\frac{x}{6})
limit as x approaches-infinity of x^4	\lim\:_{x\to\:-\infty\:}(x^{4})
tangent of f(x)=4x^3+3x,\at x=-4,-1	tangent\:f(x)=4x^{3}+3x,\at\:x=-4,-1
y^'+y/t =6cos(5t)	y^{\prime\:}+\frac{y}{t}=6\cos(5t)
integral of x^2(x^3+8)^{11}	\int\:x^{2}(x^{3}+8)^{11}dx
limit as x approaches 0 of 2x^2-3	\lim\:_{x\to\:0}(2x^{2}-3)
integral from 6 to 12 of 6e^x	\int\:_{6}^{12}6e^{x}dx
y^'=(e^{t-y})/(1+e^t)	y^{\prime\:}=\frac{e^{t-y}}{1+e^{t}}
limit as x approaches infinity of e^{-pi}	\lim\:_{x\to\:\infty\:}(e^{-π})
derivative of (3-x^2/(2x+2))	\frac{d}{dx}(\frac{3-x^{2}}{2x+2})
derivative of (\sqrt[3]{x}/(x^2))	\frac{d}{dx}(\frac{\sqrt[3]{x}}{x^{2}})
integral of x^2e^{-x/4}	\int\:x^{2}e^{-\frac{x}{4}}dx
derivative of cos^2(8x)	\frac{d}{dx}(\cos^{2}(8x))
derivative of (5x+3)^{1/5}	derivative\:(5x+3)^{\frac{1}{5}}
derivative of f(x)=-3/(x^2)	derivative\:f(x)=-\frac{3}{x^{2}}
integral of 14cos(x)	\int\:14\cos(x)dx
x^'+4x=0	x^{\prime\:}+4x=0
integral of e^{-22x}	\int\:e^{-22x}dx
derivative of y=108-90e^{-0.4t}	derivative\:y=108-90e^{-0.4t}
f(x)=x^2e^x-2xe^x+8e^x	f(x)=x^{2}e^{x}-2xe^{x}+8e^{x}
limit as h approaches 0 of ((1+h)-(1))/h	\lim\:_{h\to\:0}(\frac{(1+h)-(1)}{h})
(dy)/(dx)=-y-8	\frac{dy}{dx}=-y-8
derivative of g(x)=7e^xsqrt(x)	derivative\:g(x)=7e^{x}\sqrt{x}
derivative of sin(x^2+4)	derivative\:\sin(x^{2}+4)
sum from n=1 to infinity of (x^n)/(14^n)	\sum\:_{n=1}^{\infty\:}\frac{x^{n}}{14^{n}}
integral of 5x-2	\int\:5x-2dx
limit as x approaches-infinity of ((-x+sqrt(x^2-8)))/(6x-7)	\lim\:_{x\to\:-\infty\:}(\frac{(-x+\sqrt{x^{2}-8})}{6x-7})
derivative of x+2sin(x)	derivative\:x+2\sin(x)
limit as x approaches 0 of 3x	\lim\:_{x\to\:0}(3x)
laplacetransform e^{-2(2t-4)}(1/2 (2t-4)+2)	laplacetransform\:e^{-2(2t-4)}(\frac{1}{2}(2t-4)+2)
integral of-e^ysin(y)cos(y)	\int\:-e^{y}\sin(y)\cos(y)dy
integral of (1/(z^3)-3/(z^2))	\int\:(\frac{1}{z^{3}}-\frac{3}{z^{2}})dz
(\partial)/(\partial y)(x^2+4y^2)	\frac{\partial\:}{\partial\:y}(x^{2}+4y^{2})
(dy)/(dx)=y+e^x	\frac{dy}{dx}=y+e^{x}
integral of sqrt((4-x^2)/(x^2))	\int\:\sqrt{\frac{4-x^{2}}{x^{2}}}dx
integral from 0 to 11 of xsqrt(11-x)	\int\:_{0}^{11}x\sqrt{11-x}dx
limit as x approaches 3 of 5x^3	\lim\:_{x\to\:3}(5x^{3})
limit as x approaches-1 of e^{x+1}	\lim\:_{x\to\:-1}(e^{x+1})
derivative of 10x(x^2+6)^4	derivative\:10x(x^{2}+6)^{4}
limit as x approaches 2-of sqrt(x(x-1))	\lim\:_{x\to\:2-}(\sqrt{x(x-1)})
integral of 1/(sqrt(25-x))	\int\:\frac{1}{\sqrt{25-x}}dx
sum from n=1 to infinity of (2x)^n	\sum\:_{n=1}^{\infty\:}(2x)^{n}
(\partial)/(\partial x)(y^2-3x^3)	\frac{\partial\:}{\partial\:x}(y^{2}-3x^{3})
laplacetransform 4+t^6	laplacetransform\:4+t^{6}
derivative of f(x)=-5x	derivative\:f(x)=-5x
y^{'''}-7y^'+6y=e^{3x}	y^{\prime\:\prime\:\prime\:}-7y^{\prime\:}+6y=e^{3x}
derivative of 1-sqrt(x^2+y^2)	\frac{d}{dx}(1-\sqrt{x^{2}+y^{2}})
integral of (x+1)/(3x+2)	\int\:\frac{x+1}{3x+2}dx
integral from-3 to 1 of x	\int\:_{-3}^{1}xdx
limit as x approaches infinity of 2ln(x)	\lim\:_{x\to\:\infty\:}(2\ln(x))
limit as x approaches-6 of 5x^2+6x+a	\lim\:_{x\to\:-6}(5x^{2}+6x+a)
integral from 0 to e of 1/(x+e)	\int\:_{0}^{e}\frac{1}{x+e}dx
integral of x/(1+9x^2)	\int\:\frac{x}{1+9x^{2}}dx
inverse oflaplace (e^{-2s})/(s-9)	inverselaplace\:\frac{e^{-2s}}{s-9}
integral of cos^3(3x)sin^3(3x)	\int\:\cos^{3}(3x)\sin^{3}(3x)dx
derivative of f(x)=(e^x+x^pi)(x^2+x+1)	derivative\:f(x)=(e^{x}+x^{π})(x^{2}+x+1)
y^'=0.1y(10-y)	y^{\prime\:}=0.1y(10-y)
(\partial)/(\partial x)(ln(a/x))	\frac{\partial\:}{\partial\:x}(\ln(\frac{a}{x}))
integral from 0 to 5 of 5	\int\:_{0}^{5}5dx
sum from n=6 to infinity of 5/(n^2-25)	\sum\:_{n=6}^{\infty\:}\frac{5}{n^{2}-25}
derivative of sqrt((x^2(y^2-9)))	\frac{d}{dx}(\sqrt{(x^{2})(y^{2}-9)})
derivative of sqrt(x/3)	derivative\:\sqrt{\frac{x}{3}}
integral of (-4x^6-3x^5+5e^x)	\int\:(-4x^{6}-3x^{5}+5e^{x})dx
derivative of x^3+3x^2-6x-8	\frac{d}{dx}(x^{3}+3x^{2}-6x-8)
integral of ((arctan(x))^7)/(x^2+1)	\int\:\frac{(\arctan(x))^{7}}{x^{2}+1}dx
integral of 4\sqrt[3]{x}ln(x)	\int\:4\sqrt[3]{x}\ln(x)dx
derivative of f(x)=3x^2e^x+e^x(x^3+3)	derivative\:f(x)=3x^{2}e^{x}+e^{x}(x^{3}+3)
integral of 4x^2sqrt(x+9)	\int\:4x^{2}\sqrt{x+9}dx
integral of cot(θ/7)	\int\:\cot(\frac{θ}{7})dθ
integral of 13z^3e^z	\int\:13z^{3}e^{z}dz
limit as d approaches 0 of 1/(x+6)+d	\lim\:_{d\to\:0}(\frac{1}{x+6}+d)
(\partial)/(\partial y)(xsin(x/y))	\frac{\partial\:}{\partial\:y}(x\sin(\frac{x}{y}))
integral of xsin(3ax)	\int\:x\sin(3ax)dx
(\partial)/(\partial x)(xln(z^4+x^3))	\frac{\partial\:}{\partial\:x}(x\ln(z^{4}+x^{3}))
tangent of f(x)=((x+3)/(x-3))^2,\at x=4	tangent\:f(x)=(\frac{x+3}{x-3})^{2},\at\:x=4
derivative of ln(((1-x)/(1+x)))	\frac{d}{dx}(\ln(\frac{(1-x)}{1+x}))
integral from 1 to 9 of pi(sqrt(x-1))^2	\int\:_{1}^{9}π(\sqrt{x-1})^{2}dx
limit as s approaches 0 of 3/(s*(s+2))	\lim\:_{s\to\:0}(\frac{3}{s\cdot\:(s+2)})

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