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Popular Calculus Problems

(dx}{dy}=(\frac{y+1)/x)2	\frac{dx}{dy}=(\frac{y+1}{x})2
((x+1)dy)/(dx)+(x+2)y=2xe^{-x}	\frac{(x+1)dy}{dx}+(x+2)y=2xe^{-x}
(\partial)/(\partial x)(sin(xy)+x+y)	\frac{\partial\:}{\partial\:x}(\sin(xy)+x+y)
integral of sqrt(1-sin(2x))	\int\:\sqrt{1-\sin(2x)}dx
sum from n=0 to infinity of (-10/11)^n	\sum\:_{n=0}^{\infty\:}(-\frac{10}{11})^{n}
7t(dy)/(dt)+y=0,y(1)=1	7t\frac{dy}{dt}+y=0,y(1)=1
integral of c/x	\int\:\frac{c}{x}dx
integral of 3x^2-4x+5	\int\:3x^{2}-4x+5dx
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
tangent of y=7x^2-x^3	tangent\:y=7x^{2}-x^{3}
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
limit as x approaches 4 of 1/(x^2-16)	\lim\:_{x\to\:4}(\frac{1}{x^{2}-16})
slope of 2t^3	slope\:2t^{3}
(\partial)/(\partial x)(1/(x^2)-1/(1-x-y))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}}-\frac{1}{1-x-y})
tangent of 2x^2-3	tangent\:2x^{2}-3
laplacetransform e^{-s}	laplacetransform\:e^{-s}
y^{''}-2y^'-3y=-5te^{-t}	y^{\prime\:\prime\:}-2y^{\prime\:}-3y=-5te^{-t}
derivative of f(x)=12	derivative\:f(x)=12
limit as x approaches-3 of x+7	\lim\:_{x\to\:-3}(x+7)
integral of ln(a^2+x^2)	\int\:\ln(a^{2}+x^{2})dx
y^{''}+8y^'=0	y^{\prime\:\prime\:}+8y^{\prime\:}=0
derivative of x^3-2x^2	\frac{d}{dx}(x^{3}-2x^{2})
derivative of f(x)=3-(18)/(5x^{1/10)}	derivative\:f(x)=3-\frac{18}{5x^{\frac{1}{10}}}
integral of 1/(x^2-2x+17)	\int\:\frac{1}{x^{2}-2x+17}dx
inverse oflaplace (3-2s)/(s^2+4s+5)	inverselaplace\:\frac{3-2s}{s^{2}+4s+5}
(\partial)/(\partial x)(ln(2x+2))	\frac{\partial\:}{\partial\:x}(\ln(2x+2))
derivative of-3/(2(1+x^{3/2)})	\frac{d}{dx}(-\frac{3}{2(1+x)^{\frac{3}{2}}})
derivative of 1ln(x-(x^2)/8)	\frac{d}{dx}(1\ln(x)-\frac{x^{2}}{8})
derivative of g(u)=sqrt(6u)+sqrt(5u)	derivative\:g(u)=\sqrt{6u}+\sqrt{5u}
integral of 4/5-1/(3sqrt(5x))	\int\:\frac{4}{5}-\frac{1}{3\sqrt{5x}}dx
integral of 12θsec^2(θ)	\int\:12θ\sec^{2}(θ)dθ
maclaurin xe^{-x}	maclaurin\:xe^{-x}
(dy)/(dx)+3x^2y=10x^2	\frac{dy}{dx}+3x^{2}y=10x^{2}
xy+y^'=4x	xy+y^{\prime\:}=4x
limit as x approaches+1+of 1-cos(2(x-1))	\lim\:_{x\to\:+1+}(1-\cos(2(x-1)))
(\partial)/(\partial x)(x/(y^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{y^{2}})
derivative of (tan(x))/(cos(x))	derivative\:\frac{\tan(x)}{\cos(x)}
integral of (tan(x)+1)^2	\int\:(\tan(x)+1)^{2}dx
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
inverse oflaplace 1/(s(s+1)^3)	inverselaplace\:\frac{1}{s(s+1)^{3}}
x^{''}+2x^'+5x=0,x(0)=1,x^'(0)=-1	x^{\prime\:\prime\:}+2x^{\prime\:}+5x=0,x(0)=1,x^{\prime\:}(0)=-1
derivative of y=8sqrt(x)+3x^{1/6}	derivative\:y=8\sqrt{x}+3x^{\frac{1}{6}}
integral from 0 to 1 of pi(4-1/2 x)^2	\int\:_{0}^{1}π(4-\frac{1}{2}x)^{2}dx
tangent of (2x-9)(x^2+6),\at x=3	tangent\:(2x-9)(x^{2}+6),\at\:x=3
integral from 0 to 6 of 1	\int\:_{0}^{6}1
integral of xsqrt(-7+8x-x^2)	\int\:x\sqrt{-7+8x-x^{2}}dx
limit as x approaches 7 of 6x^{-1}	\lim\:_{x\to\:7}(6x^{-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
derivative of 1/(x^2+x+1)	\frac{d}{dx}(\frac{1}{x^{2}+x+1})
derivative of f(x)=cos(tan^3(x))	derivative\:f(x)=\cos(\tan^{3}(x))
integral of 21sec^{-2}(xta)n^3x	\int\:21\sec^{-2}(xta)n^{3}xdx
d/(dθ)(e^{tan(θ)})	\frac{d}{dθ}(e^{\tan(θ)})
integral of 6/(2x+3x^2)	\int\:\frac{6}{2x+3x^{2}}dx
integral of (x^2+5)/(x^3-x^2+x+3)	\int\:\frac{x^{2}+5}{x^{3}-x^{2}+x+3}dx
derivative of (e^x/(9e^x+x^2))	\frac{d}{dx}(\frac{e^{x}}{9e^{x}+x^{2}})
integral from 2 to 3 of 3	\int\:_{2}^{3}3dx
area-x^2+10x-16,2x-4,2,8	area\:-x^{2}+10x-16,2x-4,2,8
derivative of-5x^3ln(x)	derivative\:-5x^{3}\ln(x)
integral of-e^{-x} 1/x	\int\:-e^{-x}\frac{1}{x}dx
y(x+3)+y^'=0,y(-6)=1	y(x+3)+y^{\prime\:}=0,y(-6)=1
derivative of 2arcsin(x-1)	\frac{d}{dx}(2\arcsin(x-1))
integral of (2e^{5x})	\int\:(2e^{5x})dx
derivative of x/((x+1)^2)	derivative\:\frac{x}{(x+1)^{2}}
(dy}{dx}=(\frac{4y)/x)	\frac{dy}{dx}=(\frac{4y}{x})
derivative of arctan(x/y)	\frac{d}{dx}(\arctan(\frac{x}{y}))
-1/4 dv=v^2dx	-\frac{1}{4}dv=v^{2}dx
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 e^{tan(2x})	\frac{d}{dx}(e^{\tan(2x)})
derivative of (2x-5/(3x-1))	\frac{d}{dx}(\frac{2x-5}{3x-1})
limit as x approaches 2 of 5x^4-5x^3+5	\lim\:_{x\to\:2}(5x^{4}-5x^{3}+5)
area y=x^2,y=3-x	area\:y=x^{2},y=3-x
derivative of ln(((x+1)/x))	\frac{d}{dx}(\ln(\frac{(x+1)}{x}))
integral of e^{x/(y^2)}	\int\:e^{\frac{x}{y^{2}}}dx
integral of (tan(ln(3x+2)))/(3x+2)	\int\:\frac{\tan(\ln(3x+2))}{3x+2}dx
integral from 0 to 4 of ((t^2)/3+2t)	\int\:_{0}^{4}(\frac{t^{2}}{3}+2t)dt
integral of 1/(9-8x)	\int\:\frac{1}{9-8x}dx
integral of (xe^{3x})/((1+3x)^2)	\int\:\frac{xe^{3x}}{(1+3x)^{2}}dx
integral of \sqrt[3]{tan(x)}sec^2(x)	\int\:\sqrt[3]{\tan(x)}\sec^{2}(x)dx
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}}
integral of sec^4(x)	\int\:\sec^{4}(x)dx
tangent of f(x)=60+20x-4.5x^2,\at x=2	tangent\:f(x)=60+20x-4.5x^{2},\at\:x=2
area-x^2-x+9,-x+7,0	area\:-x^{2}-x+9,-x+7,0
integral of sin^3(3x)cos^4(3x)	\int\:\sin^{3}(3x)\cos^{4}(3x)dx
(\partial)/(\partial x)((1-x)(1-y))	\frac{\partial\:}{\partial\:x}((1-x)(1-y))
limit as x approaches 4+of (x-4)/(x^2-1)	\lim\:_{x\to\:4+}(\frac{x-4}{x^{2}-1})
derivative of f(x)=3x^6+9x^2-7	derivative\:f(x)=3x^{6}+9x^{2}-7
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-11sin(x)	\frac{d}{dx}(-11\sin(x))
limit as x approaches-4-of x/(x+4)	\lim\:_{x\to\:-4-}(\frac{x}{x+4})

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