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Popular Calculus Problems

integral from 0 to 9 of x^2	\int\:_{0}^{9}x^{2}dx
(\partial)/(\partial y)(y^3sin(4x))	\frac{\partial\:}{\partial\:y}(y^{3}\sin(4x))
integral of xcsch^2((x^2)/2)	\int\:x\csch^{2}(\frac{x^{2}}{2})dx
derivative of ((x^2-1))/((x^2+x+1))	derivative\:\frac{(x^{2}-1)}{(x^{2}+x+1)}
derivative of f(x)=(8(x^3-6x^2+12x))	derivative\:f(x)=(8(x^{3}-6x^{2}+12x))
(\partial)/(\partial x)((cos(x^2*y))/(z^3))	\frac{\partial\:}{\partial\:x}(\frac{\cos(x^{2}\cdot\:y)}{z^{3}})
implicit (dy)/(dx),5xy^5+3xy=24	implicit\:\frac{dy}{dx},5xy^{5}+3xy=24
derivative of arctan(x/6)	derivative\:\arctan(\frac{x}{6})
(\partial)/(\partial x)(pi*xsqrt(x^2+y^2))	\frac{\partial\:}{\partial\:x}(π\cdot\:x\sqrt{x^{2}+y^{2}})
derivative of ln(1/(6+x))	\frac{d}{dx}(\ln(\frac{1}{6+x}))
limit as x approaches 3 of sqrt(x+1)	\lim\:_{x\to\:3}(\sqrt{x+1})
integral of sech^2(x)	\int\:\sech^{2}(x)dx
laplacetransform 1/2 (t-2)^2	laplacetransform\:\frac{1}{2}(t-2)^{2}
(\partial)/(\partial x)(4y+xe^{x/y})	\frac{\partial\:}{\partial\:x}(4y+xe^{\frac{x}{y}})
integral of 7sec^2(x)	\int\:7\sec^{2}(x)dx
integral of e^{5x}x	\int\:e^{5x}xdx
integral of 2/(xsqrt(9x^2+1))	\int\:\frac{2}{x\sqrt{9x^{2}+1}}dx
integral of (x^2+5x+7)/(x+3)	\int\:\frac{x^{2}+5x+7}{x+3}dx
inverse oflaplace (4se^{-3s})/((s^2+4))	inverselaplace\:\frac{4se^{-3s}}{(s^{2}+4)}
implicit (dy)/(dx),y=2x-5	implicit\:\frac{dy}{dx},y=2x-5
sum from n=1 to infinity of arctan(4n)	\sum\:_{n=1}^{\infty\:}\arctan(4n)
inverse oflaplace (2s^2+1)/(s+3)	inverselaplace\:\frac{2s^{2}+1}{s+3}
(xdy)/(dx)=y+xe^{-y/x}	\frac{xdy}{dx}=y+xe^{-\frac{y}{x}}
derivative of (ln(x+3x)^2)	\frac{d}{dx}((\ln(x)+3x)^{2})
(\partial)/(\partial x)(ln(x+9y+2z))	\frac{\partial\:}{\partial\:x}(\ln(x+9y+2z))
derivative of 2tan(x+pi/(12))	\frac{d}{dx}(2\tan(x+\frac{π}{12}))
derivative of (x+1^{2/3}(3x^2-2)^3)	\frac{d}{dx}((x+1)^{\frac{2}{3}}(3x^{2}-2)^{3})
integral of (sec(2x)tan(2x))	\int\:(\sec(2x)\tan(2x))dx
integral of (m^3)/((z^2)^3)	\int\:\frac{m^{3}}{(z^{2})^{3}}dm
(\partial)/(\partial y)(xe^{xy})	\frac{\partial\:}{\partial\:y}(xe^{xy})
integral of ((ln(x))^3)/(3x)	\int\:\frac{(\ln(x))^{3}}{3x}dx
sum from n=0 to infinity of (nx^n)/(n+8)	\sum\:_{n=0}^{\infty\:}\frac{nx^{n}}{n+8}
integral of (3x)/(2x^2+3x+4)	\int\:\frac{3x}{2x^{2}+3x+4}dx
(\partial)/(\partial x)(2x^{6y})	\frac{\partial\:}{\partial\:x}(2x^{6y})
integral of exsin(x)	\int\:ex\sin(x)dx
slope of (sqrt(x))/(sqrt(2))	slope\:\frac{\sqrt{x}}{\sqrt{2}}
derivative of Ce^{2x}	\frac{d}{dx}(Ce^{2x})
(4+t^2)((dy)/(dt))+2ty=4t	(4+t^{2})(\frac{dy}{dt})+2ty=4t
derivative of-xsin(xy)	\frac{d}{dx}(-x\sin(xy))
2x(dy)/(dx)=y+1	2x\frac{dy}{dx}=y+1
integral from 4 to 6 of 0.2e^{-0.2x}	\int\:_{4}^{6}0.2e^{-0.2x}dx
limit as x approaches 3 of (sin(3x))/x	\lim\:_{x\to\:3}(\frac{\sin(3x)}{x})
integral of x/((x^2+6)^2)	\int\:\frac{x}{(x^{2}+6)^{2}}dx
(\partial)/(\partial x)(3e^{sin(x+4ct)})	\frac{\partial\:}{\partial\:x}(3e^{\sin(x+4ct)})
((x+1)dy)/(dx)+(x+2)y=2xe^{-x}	\frac{(x+1)dy}{dx}+(x+2)y=2xe^{-x}
integral of c/x	\int\:\frac{c}{x}dx
limit as x approaches 0.1 of (e^{5x}-1)/x	\lim\:_{x\to\:0.1}(\frac{e^{5x}-1}{x})
4y^{''}+36y^'+81y=0	4y^{\prime\:\prime\:}+36y^{\prime\:}+81y=0
tangent of-3x^2+6x-2	tangent\:-3x^{2}+6x-2
f^'(x)=sec(2x)tan(2x)	f^{\prime\:}(x)=\sec(2x)\tan(2x)
(dy)/(dx)=2y(3-x)	\frac{dy}{dx}=2y(3-x)
integral of (x^2)/(x^2-3x+2)	\int\:\frac{x^{2}}{x^{2}-3x+2}dx
derivative of f(x)=12	derivative\:f(x)=12
derivative of f(x)=3-(18)/(5x^{1/10)}	derivative\:f(x)=3-\frac{18}{5x^{\frac{1}{10}}}
derivative of g(u)=sqrt(6u)+sqrt(5u)	derivative\:g(u)=\sqrt{6u}+\sqrt{5u}
integral of 12θsec^2(θ)	\int\:12θ\sec^{2}(θ)dθ
derivative of 4x^2-2x(-9)	derivative\:4x^{2}-2x(-9)
integral of (2x+3)/(x^2-9)	\int\:\frac{2x+3}{x^{2}-9}dx
derivative of xsqrt(25-x^2)	\frac{d}{dx}(x\sqrt{25-x^{2}})
integral of (3x-4)/((x-1)(x+2))	\int\:\frac{3x-4}{(x-1)(x+2)}dx
x^{''}+2x^'+5x=0,x(0)=1,x^'(0)=-1	x^{\prime\:\prime\:}+2x^{\prime\:}+5x=0,x(0)=1,x^{\prime\:}(0)=-1
limit as x approaches 2 of 3x^2-2x+4	\lim\:_{x\to\:2}(3x^{2}-2x+4)
integral of (x^3+x)^8(3x^2+1)	\int\:(x^{3}+x)^{8}(3x^{2}+1)dx
integral of 6/(2x+3x^2)	\int\:\frac{6}{2x+3x^{2}}dx
derivative of (e^x/(9e^x+x^2))	\frac{d}{dx}(\frac{e^{x}}{9e^{x}+x^{2}})
area-x^2+10x-16,2x-4,2,8	area\:-x^{2}+10x-16,2x-4,2,8
derivative of 2arcsin(x-1)	\frac{d}{dx}(2\arcsin(x-1))
inverse oflaplace (20)/(s(s^2+6s+144))	inverselaplace\:\frac{20}{s(s^{2}+6s+144)}
area y= 3/x ,y= 3/(x^2),x=4	area\:y=\frac{3}{x},y=\frac{3}{x^{2}},x=4
derivative of f(x)=800-800x^{-1}	derivative\:f(x)=800-800x^{-1}
derivative of y=(2x+5)/(sqrt(x))	derivative\:y=\frac{2x+5}{\sqrt{x}}
derivative of arccos(-x/5)	\frac{d}{dx}(\arccos(-\frac{x}{5}))
(sin(x)-ysin(x)-2cos(x))+cos(x)y^'=0,y(0)=-1	(\sin(x)-y\sin(x)-2\cos(x))+\cos(x)y^{\prime\:}=0,y(0)=-1
derivative of f(x)=x^2-5x+5	derivative\:f(x)=x^{2}-5x+5
slope of y=9+5x^2-2x^3	slope\:y=9+5x^{2}-2x^{3}
(\partial)/(\partial x)(x/(1+x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{1+x^{2}+y^{2}})
area y=4x^2,y=4	area\:y=4x^{2},y=4
integral of (2x-3)/(sqrt(x^2+6x+4))	\int\:\frac{2x-3}{\sqrt{x^{2}+6x+4}}dx
derivative of 13e^x	\frac{d}{dx}(13e^{x})
(x^2+1)y^'+4x(y-1)=0,y(0)=3	(x^{2}+1)y^{\prime\:}+4x(y-1)=0,y(0)=3
(dy)/(dx)+y^3x+8y=0	\frac{dy}{dx}+y^{3}x+8y=0
integral of sin^5(9x)	\int\:\sin^{5}(9x)dx
derivative of-2/((x-1^2))	\frac{d}{dx}(-\frac{2}{(x-1)^{2}})
sum from n=1 to infinity of 1/(8^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{8^{n}}
derivative of f(x)=x^2+6x	derivative\:f(x)=x^{2}+6x
integral of 1/(sqrt(1-16x^2))	\int\:\frac{1}{\sqrt{1-16x^{2}}}dx
derivative of e^{cot(4x)}	derivative\:e^{\cot(4x)}
derivative of (6x^2+8x+8x)/(sqrt(x))	derivative\:\frac{6x^{2}+8x+8x}{\sqrt{x}}
y^'=((y^2+2xy))/(x^2)	y^{\prime\:}=\frac{(y^{2}+2xy)}{x^{2}}
integral of e^{3x}sin(3x)	\int\:e^{3x}\sin(3x)dx
y^'= x/y ,y(0)=3	y^{\prime\:}=\frac{x}{y},y(0)=3
derivative of (18x+4x^2/((9+4x)^2))	\frac{d}{dx}(\frac{18x+4x^{2}}{(9+4x)^{2}})
integral of sin(t^2)	\int\:\sin(t^{2})dt
laplacetransform 1-cos(2t)	laplacetransform\:1-\cos(2t)
roots xsin(y)	roots\:x\sin(y)
f^'(x)= x/8-1	f^{\prime\:}(x)=\frac{x}{8}-1
slope of y=2-x^3,P(1,1)	slope\:y=2-x^{3},P(1,1)
implicit (dy)/(dx),e x/y =8x-y	implicit\:\frac{dy}{dx},e\frac{x}{y}=8x-y
derivative of 3arcsin(x^3)	\frac{d}{dx}(3\arcsin(x^{3}))
derivative of e^{2x}(2-x)	\frac{d}{dx}(e^{2x}(2-x))

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