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Popular Calculus Problems

(\partial)/(\partial x)(0.5ln(x)+0.5ln(y))	\frac{\partial\:}{\partial\:x}(0.5\ln(x)+0.5\ln(y))
integral of e^{8t}	\int\:e^{8t}dt
(\partial)/(\partial y)((x+y)e^{x+2y})	\frac{\partial\:}{\partial\:y}((x+y)e^{x+2y})
laplacetransform t^2-2t	laplacetransform\:t^{2}-2t
derivative of-7/(\sqrt[4]{x)}	derivative\:-\frac{7}{\sqrt[4]{x}}
integral of (x^4)/(8-x^5)	\int\:\frac{x^{4}}{8-x^{5}}dx
(x+ye^{y/x})dx-xe^{y/x}dy=0	(x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0
integral from-1 to 1 of e^y-y^2+6	\int\:_{-1}^{1}e^{y}-y^{2}+6dy
integral of (4x)/(x^4+1)	\int\:\frac{4x}{x^{4}+1}dx
integral of 25x^2	\int\:25x^{2}dx
derivative of ce^{-x}	\frac{d}{dx}(ce^{-x})
2t(dy)/(dt)+y=t^3	2t\frac{dy}{dt}+y=t^{3}
derivative of ((x^2-8x-17))/((x+2))	derivative\:\frac{(x^{2}-8x-17)}{(x+2)}
derivative of sqrt(cos(e^{x^4cos(x)))}	derivative\:\sqrt{\cos(e^{x^{4}\cos(x)})}
integral of cot^5(2t)	\int\:\cot^{5}(2t)dt
derivative of y= 1/2 \sqrt[3]{x}	derivative\:y=\frac{1}{2}\sqrt[3]{x}
2y^{''}+y^'+y=0	2y^{\prime\:\prime\:}+y^{\prime\:}+y=0
derivative of t^2(5t+9)^3	derivative\:t^{2}(5t+9)^{3}
taylor 2x^3-3x^2	taylor\:2x^{3}-3x^{2}
taylor 1/(x-1),0	taylor\:\frac{1}{x-1},0
limit as x approaches 1 of (sin(x))/x	\lim\:_{x\to\:1}(\frac{\sin(x)}{x})
derivative of 3/((1-x^2)^4)	derivative\:\frac{3}{(1-x^{2})^{4}}
derivative of (1-x^2^{-2})	\frac{d}{dx}((1-x^{2})^{-2})
y^{''}+5y^'+6y=0,y(0)=1,y^'(0)=0	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=0,y(0)=1,y^{\prime\:}(0)=0
(\partial)/(\partial x)(x^{y^x})	\frac{\partial\:}{\partial\:x}(x^{y^{x}})
integral of 1/(x^2+64)	\int\:\frac{1}{x^{2}+64}dx
tangent of y=2x^3-x^2+2	tangent\:y=2x^{3}-x^{2}+2
integral of (e^{x^n})/(x^{1-n)}	\int\:\frac{e^{x^{n}}}{x^{1-n}}dx
limit as h approaches 0 of (5e^x-5e^{x+h})/(3h)	\lim\:_{h\to\:0}(\frac{5e^{x}-5e^{x+h}}{3h})
inverse oflaplace (e^{-s})/((s^2+8))	inverselaplace\:\frac{e^{-s}}{(s^{2}+8)}
derivative of (3x-1/(2x+1))	\frac{d}{dx}(\frac{3x-1}{2x+1})
y^'+4x^{-1}y=x^2,\quad y(1)=-2	y^{\prime\:}+4x^{-1}y=x^{2},\quad\:y(1)=-2
sum from n=1 to infinity of (5^n)/(n^5)	\sum\:_{n=1}^{\infty\:}\frac{5^{n}}{n^{5}}
taylor 1/(x+2),0	taylor\:\frac{1}{x+2},0
sum from k=2 to infinity of 1/k-1/(4^k)	\sum\:_{k=2}^{\infty\:}\frac{1}{k}-\frac{1}{4^{k}}
(1+ln(x)+y/x)dx-(1-ln(x))dy=0	(1+\ln(x)+\frac{y}{x})dx-(1-\ln(x))dy=0
(dy)/(dx)=2x+y	\frac{dy}{dx}=2x+y
y^'+2xy=0,y(0)=3	y^{\prime\:}+2xy=0,y(0)=3
integral of sec^6(x)tan^6(x)	\int\:\sec^{6}(x)\tan^{6}(x)dx
tangent of ln(x^4+3)	tangent\:\ln(x^{4}+3)
integral from 0 to 1 of 2pi(x)(e^{-x^2})	\int\:_{0}^{1}2π(x)(e^{-x^{2}})dx
derivative of (3-x)^2	derivative\:(3-x)^{2}
derivative of e^x-cot(x)	derivative\:e^{x}-\cot(x)
inverse oflaplace 1/((s(s^2+s+1)))	inverselaplace\:\frac{1}{(s(s^{2}+s+1))}
integral of 1/(4e^{-2x)+e^{2x}}	\int\:\frac{1}{4e^{-2x}+e^{2x}}dx
(dy)/(dx)=((x^3+2y^3))/(xy^2)	\frac{dy}{dx}=\frac{(x^{3}+2y^{3})}{xy^{2}}
taylor x^{(1/2)}	taylor\:x^{(\frac{1}{2})}
limit as x approaches 0+of 2x-1	\lim\:_{x\to\:0+}(2x-1)
derivative of nln(1/x)	\frac{d}{dx}(n\ln(\frac{1}{x}))
(\partial)/(\partial x)((47x^2)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{47x^{2}}{(x-y)^{2}})
integral of x/(sqrt(x^2+y^2))	\int\:\frac{x}{\sqrt{x^{2}+y^{2}}}dx
limit as x approaches 0+of 0^x	\lim\:_{x\to\:0+}(0^{x})
y^'=y(xy^5+5)	y^{\prime\:}=y(xy^{5}+5)
integral of sec^4(x)tan^6(x)	\int\:\sec^{4}(x)\tan^{6}(x)dx
t^2((dy)/(dt))+y=0	t^{2}(\frac{dy}{dt})+y=0
(\partial)/(\partial y)(ye^z)	\frac{\partial\:}{\partial\:y}(ye^{z})
(dy)/(dx)+xy=xy^{-3}	\frac{dy}{dx}+xy=xy^{-3}
limit as x approaches-4pi of 1+csc(x)	\lim\:_{x\to\:-4π}(1+\csc(x))
area x^2-6x,-x^2+2x	area\:x^{2}-6x,-x^{2}+2x
derivative of y=x-6	derivative\:y=x-6
integral of 5x^4-7x^6-3x^2	\int\:5x^{4}-7x^{6}-3x^{2}dx
(\partial}{\partial u}(\frac{v+u)/2)	\frac{\partial\:}{\partial\:u}(\frac{v+u}{2})
derivative of 3x^3y	\frac{d}{dx}(3x^{3}y)
integral from 0 to 3 of 1/(sqrt(x))	\int\:_{0}^{3}\frac{1}{\sqrt{x}}dx
integral from 0 to t of xe^{-x}	\int\:_{0}^{t}xe^{-x}dx
xy^'-y=2x^2-2x-2	xy^{\prime\:}-y=2x^{2}-2x-2
xy^'-y=x,y(1)=10	xy^{\prime\:}-y=x,y(1)=10
integral from 0 to 2 of pi(3x^2)^2	\int\:_{0}^{2}π(3x^{2})^{2}dx
(\partial)/(\partial x)(4x^2+3y^4)	\frac{\partial\:}{\partial\:x}(4x^{2}+3y^{4})
limit as x approaches 1-of 1/x-1	\lim\:_{x\to\:1-}(\frac{1}{x}-1)
y^{''}+9y=3sec(3t)	y^{\prime\:\prime\:}+9y=3\sec(3t)
f(x)=cos(x^2)*2x	f(x)=\cos(x^{2})\cdot\:2x
area y=x+1,y=9-x^2,x=-1,x=2	area\:y=x+1,y=9-x^{2},x=-1,x=2
integral of (sin^4(x)cos^2(x))	\int\:(\sin^{4}(x)\cos^{2}(x))dx
integral of (4x^2+3x+4)/((x^2+1)^2)	\int\:\frac{4x^{2}+3x+4}{(x^{2}+1)^{2}}dx
integral from-1 to 0 of (30e^{1/x})/(x^3)	\int\:_{-1}^{0}\frac{30e^{\frac{1}{x}}}{x^{3}}dx
area 11-x-2x^2, 8/(x^3)	area\:11-x-2x^{2},\frac{8}{x^{3}}
integral of 4/(x^2)	\int\:\frac{4}{x^{2}}dx
derivative of f(x)=2e^{3-4x}	derivative\:f(x)=2e^{3-4x}
integral from 0 to pi of 7sin^2(xco)s^4x	\int\:_{0}^{π}7\sin^{2}(xco)s^{4}xdx
3y^{''}-y^'+2y=0,y(0)=5,y^'(0)=0	3y^{\prime\:\prime\:}-y^{\prime\:}+2y=0,y(0)=5,y^{\prime\:}(0)=0
sum from n=0 to infinity of (n^4)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{4}}{3^{n}}
(\partial)/(\partial z)(rsin(t))	\frac{\partial\:}{\partial\:z}(r\sin(t))
integral of e^{2t}sin(3t)	\int\:e^{2t}\sin(3t)dt
derivative of arctan(cos(7x))	derivative\:\arctan(\cos(7x))
derivative of sqrt(x)+sqrt(y)+6	derivative\:\sqrt{x}+\sqrt{y}+6
integral from 0 to 8 of e^{-0.25t}	\int\:_{0}^{8}e^{-0.25t}dt
integral of sin(3x)sin(6x)	\int\:\sin(3x)\sin(6x)dx
derivative of [x^2(x^2+8x)]^6	derivative\:[x^{2}(x^{2}+8x)]^{6}
x^2(dy)/(dx)=y^2	x^{2}\frac{dy}{dx}=y^{2}
derivative of (x^4)/(16)+1/(2x^2)	derivative\:\frac{x^{4}}{16}+\frac{1}{2x^{2}}
integral of 1/(sqrt(16-4x^2))	\int\:\frac{1}{\sqrt{16-4x^{2}}}dx
integral of 1/(2y+1)	\int\:\frac{1}{2y+1}dy
limit as x approaches infinity of (-3)/x	\lim\:_{x\to\:\infty\:}(\frac{-3}{x})
inverse oflaplace 1/(s(s^2+1))	inverselaplace\:\frac{1}{s(s^{2}+1)}
limit as x approaches-2 of 4x^2	\lim\:_{x\to\:-2}(4x^{2})
derivative of x^2-16	\frac{d}{dx}(x^{2}-16)
integral of (0.7y^3+10+2y^{-3})	\int\:(0.7y^{3}+10+2y^{-3})dy
derivative of f(x)=x^2-2x-3	derivative\:f(x)=x^{2}-2x-3
derivative of sin(cot(x))	\frac{d}{dx}(\sin(\cot(x)))

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