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Popular Calculus Problems

integral of 1/(z^2-1)	\int\:\frac{1}{z^{2}-1}dz
derivative of f(x)=(6x^2-10x)e^x	derivative\:f(x)=(6x^{2}-10x)e^{x}
integral of (sec^2(θ)+5)	\int\:(\sec^{2}(θ)+5)dθ
(dy)/(dx)+y^9x+7y=0	\frac{dy}{dx}+y^{9}x+7y=0
integral of (2x^2+3)/(x^3)	\int\:\frac{2x^{2}+3}{x^{3}}dx
(\partial)/(\partial x)(2x^2y-x^3)	\frac{\partial\:}{\partial\:x}(2x^{2}y-x^{3})
sum from n=1 to infinity of 2/(3^{n+1)}	\sum\:_{n=1}^{\infty\:}\frac{2}{3^{n+1}}
inverse oflaplace 1/S	inverselaplace\:\frac{1}{S}
integral of ((4-2x))/((x+1)(x-1)^2)	\int\:\frac{(4-2x)}{(x+1)(x-1)^{2}}dx
integral from 1 to infinity of 3/(x^2)	\int\:_{1}^{\infty\:}\frac{3}{x^{2}}dx
limit as x approaches-4 of x^2-8	\lim\:_{x\to\:-4}(x^{2}-8)
integral of 1/((3x+5)^3)	\int\:\frac{1}{(3x+5)^{3}}dx
f(x)=2x^3-9x^2+12x-6	f(x)=2x^{3}-9x^{2}+12x-6
(dy)/(dt)=k(y-20)	\frac{dy}{dt}=k(y-20)
inverse oflaplace ((1-e^{-3s}))/s	inverselaplace\:\frac{(1-e^{-3s})}{s}
derivative of csc^4(2x)	\frac{d}{dx}(\csc^{4}(2x))
integral of (y^{n-1})/((ay^n+b)^m)	\int\:\frac{y^{n-1}}{(ay^{n}+b)^{m}}dy
f(x)=10x	f(x)=10x
slope of (9,-2),(-3,2)	slope\:(9,-2),(-3,2)
integral of (sin(x)+cos(x))	\int\:(\sin(x)+\cos(x))dx
integral from 4 to 7 of x^4ln(2x)	\int\:_{4}^{7}x^{4}\ln(2x)dx
limit as x approaches 8 of (x^8)/(x-8)	\lim\:_{x\to\:8}(\frac{x^{8}}{x-8})
integral of-(10)/(t+7)	\int\:-\frac{10}{t+7}dt
derivative of 3sqrt(x^2+8x)	\frac{d}{dx}(3\sqrt{x^{2}+8x})
(dy)/(dx)=6x^2-x^2y	\frac{dy}{dx}=6x^{2}-x^{2}y
slope of xy-3y^2=6,(9,2)	slope\:xy-3y^{2}=6,(9,2)
derivative of ln(x^3(x-1)^4)	\frac{d}{dx}(\ln(x^{3})(x-1)^{4})
integral of 2*e^{2x}	\int\:2\cdot\:e^{2x}dx
limit as x approaches 0 of 1/(sin(3x))	\lim\:_{x\to\:0}(\frac{1}{\sin(3x)})
tangent of f(x)=2x^2,\at 3	tangent\:f(x)=2x^{2},\at\:3
integral from-2 to 3 of (12)/(x^4)	\int\:_{-2}^{3}\frac{12}{x^{4}}dx
tangent of f(x)=sin(sin(x)),\at x=3pi	tangent\:f(x)=\sin(\sin(x)),\at\:x=3π
integral of x^9e^{7x^5}	\int\:x^{9}e^{7x^{5}}dx
integral of x^3-2x+2	\int\:x^{3}-2x+2dx
integral of (1+x^2)/(sqrt(x))	\int\:\frac{1+x^{2}}{\sqrt{x}}dx
integral of log_{4}(3x+1)	\int\:\log_{4}(3x+1)dx
3y^{''}+2y^'-y=0	3y^{\prime\:\prime\:}+2y^{\prime\:}-y=0
integral of x(2x+1)e^{4x^3+3x^2-4}	\int\:x(2x+1)e^{4x^{3}+3x^{2}-4}dx
y^'+y^2=1	y^{\prime\:}+y^{2}=1
derivative of ((4x^5+5))/(x^3)	derivative\:\frac{(4x^{5}+5)}{x^{3}}
x(dy)/(dx)+6y=1-4/x	x\frac{dy}{dx}+6y=1-\frac{4}{x}
integral of sec^7(2x)tan(2x)	\int\:\sec^{7}(2x)\tan(2x)dx
integral of ((x+1)^4)/((x^2+2x+2)^3)	\int\:\frac{(x+1)^{4}}{(x^{2}+2x+2)^{3}}dx
integral of xcos^3(x^2)	\int\:x\cos^{3}(x^{2})dx
derivative of (1+5x^2(x-x^2))	\frac{d}{dx}((1+5x^{2})(x-x^{2}))
derivative of 8/(x^2)	derivative\:\frac{8}{x^{2}}
integral of (24)/(x^2-36)	\int\:\frac{24}{x^{2}-36}dx
(\partial)/(\partial x)(2^y)	\frac{\partial\:}{\partial\:x}(2^{y})
derivative of (x^2-7x+6/(x^2+7))	\frac{d}{dx}(\frac{x^{2}-7x+6}{x^{2}+7})
derivative of 2cos(pi/3)	derivative\:2\cos(\frac{π}{3})
integral of e^{-rt}	\int\:e^{-rt}dt
(sin(2θ))^'	(\sin(2θ))^{\prime\:}
limit as h approaches 0 of (sin(h))/(7h)	\lim\:_{h\to\:0}(\frac{\sin(h)}{7h})
limit as y approaches 0 of 5/(y^2+y)-5/y	\lim\:_{y\to\:0}(\frac{5}{y^{2}+y}-\frac{5}{y})
integral from 3 to infinity of 1/(x^2-1)	\int\:_{3}^{\infty\:}\frac{1}{x^{2}-1}dx
integral of 4(sin(2x))/(sin(x))	\int\:4\frac{\sin(2x)}{\sin(x)}dx
derivative of (sqrt(s)-6)/(sqrt(s)+2)	derivative\:\frac{\sqrt{s}-6}{\sqrt{s}+2}
integral from 0 to pi/3 of 81sin^2(x)	\int\:_{0}^{\frac{π}{3}}81\sin^{2}(x)dx
integral of 1/((x-2)^2(x^2+3)^2)	\int\:\frac{1}{(x-2)^{2}(x^{2}+3)^{2}}dx
derivative of e^{-x/2}cos((sqrt(3)/2 x))	\frac{d}{dx}(e^{-\frac{x}{2}}\cos(\frac{\sqrt{3}}{2}x))
derivative of-3/2 x^4cos(x)	\frac{d}{dx}(-\frac{3}{2}x^{4}\cos(x))
area x^2,x	area\:x^{2},x
integral from 0 to 5 of x^3	\int\:_{0}^{5}x^{3}dx
y^{''}x^2-5xy^'+9y=0	y^{\prime\:\prime\:}x^{2}-5xy^{\prime\:}+9y=0
laplacetransform cos^2(kt)	laplacetransform\:\cos^{2}(kt)
integral from 0 to 3 of 3	\int\:_{0}^{3}3dx
derivative of (x-ln(1+x)/(x^2))	\frac{d}{dx}(\frac{x-\ln(1+x)}{x^{2}})
integral of xln(3)	\int\:x\ln(3)dx
limit as x approaches 1+of (2-x)/(x-1)	\lim\:_{x\to\:1+}(\frac{2-x}{x-1})
y^{''}-12y^'+36y=4xe^{6x}	y^{\prime\:\prime\:}-12y^{\prime\:}+36y=4xe^{6x}
sum from n=2 to infinity of e^{3-2n}	\sum\:_{n=2}^{\infty\:}e^{3-2n}
integral of 3(3x+9)^3	\int\:3(3x+9)^{3}dx
limit as x approaches 0 of (sinh(x)-x)/(x^3)	\lim\:_{x\to\:0}(\frac{\sinh(x)-x}{x^{3}})
derivative of e^{n*x}	derivative\:e^{n\cdot\:x}
area (x^2)/4 ,(-x+6)/4 ,-3,2	area\:\frac{x^{2}}{4},\frac{-x+6}{4},-3,2
derivative of (10x+2x^2)/((5+2x)^2)	derivative\:\frac{10x+2x^{2}}{(5+2x)^{2}}
(dy)/(dt)+ay+b=0	\frac{dy}{dt}+ay+b=0
sum from n=0 to infinity of (9/10)^n	\sum\:_{n=0}^{\infty\:}(\frac{9}{10})^{n}
integral of (sqrt(1-\sqrt{w)})/(sqrt(w))	\int\:\frac{\sqrt{1-\sqrt{w}}}{\sqrt{w}}dw
integral of-e^{-x}	\int\:-e^{-x}dx
integral of x\sqrt[3]{x+10}	\int\:x\sqrt[3]{x+10}dx
integral of (x^4)/(x^2-1)	\int\:\frac{x^{4}}{x^{2}-1}dx
integral of xcos(xn)	\int\:x\cos(xn)dx
integral of sqrt(x)(6-x)	\int\:\sqrt{x}(6-x)dx
inverse oflaplace s/((s^2-k^2))	inverselaplace\:\frac{s}{(s^{2}-k^{2})}
(\partial)/(\partial x)((x^3)sqrt(x^2+9))	\frac{\partial\:}{\partial\:x}((x^{3})\sqrt{x^{2}+9})
limit as x approaches 1-of (x^2-1)/(x-1)	\lim\:_{x\to\:1-}(\frac{x^{2}-1}{x-1})
integral of x/((x+1)(x+2)^2)	\int\:\frac{x}{(x+1)(x+2)^{2}}dx
(dy)/(dx)=2y+1	\frac{dy}{dx}=2y+1
sum from n=0 to infinity of 2/(1.15^n)	\sum\:_{n=0}^{\infty\:}\frac{2}{1.15^{n}}
y^{''}+25y=-30sec(5t)	y^{\prime\:\prime\:}+25y=-30\sec(5t)
derivative of (3x^2-6/(2x+3))	\frac{d}{dx}(\frac{3x^{2}-6}{2x+3})
derivative of e^x*cos(2x)	\frac{d}{dx}(e^{x}\cdot\:\cos(2x))
derivative of tan(xsin(x))	\frac{d}{dx}(\tan(x)\sin(x))
derivative of 4xe^x	derivative\:4xe^{x}
(\partial)/(\partial y)(4x^2+y^2-800)	\frac{\partial\:}{\partial\:y}(4x^{2}+y^{2}-800)
tangent of f(x)=x^3-8x^2,\at x=0	tangent\:f(x)=x^{3}-8x^{2},\at\:x=0
integral of sec^6(x)tan^5(x)	\int\:\sec^{6}(x)\tan^{5}(x)dx
limit as x approaches 0 of (x^2)/2	\lim\:_{x\to\:0}(\frac{x^{2}}{2})
derivative of ((x^2+3x-4)/(x+2))	\frac{d}{dx}(\frac{(x^{2}+3x-4)}{x+2})

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