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Popular Calculus Problems

limit as x approaches 5 of-x^2+5x-8	\lim\:_{x\to\:5}(-x^{2}+5x-8)
integral of (cos^2(x)sin(2x))/2	\int\:\frac{\cos^{2}(x)\sin(2x)}{2}dx
integral of (ysin(x))	\int\:(y\sin(x))dx
slope of (-3,-8),(4,6)	slope\:(-3,-8),(4,6)
integral from 0 to 0.2 of 8e^{-8x}	\int\:_{0}^{0.2}8e^{-8x}dx
integral of x(e^x+e^{x^2})	\int\:x(e^{x}+e^{x^{2}})dx
area 2x^2+11,0,-2,2	area\:2x^{2}+11,0,-2,2
tangent of f(x)=x^3-2x+2,\at x=4	tangent\:f(x)=x^{3}-2x+2,\at\:x=4
derivative of ln(x+ln(x))	\frac{d}{dx}(\ln(x+\ln(x)))
derivative of 1-e^{-x/2}	\frac{d}{dx}(1-e^{-\frac{x}{2}})
slope of 1/(x-5)	slope\:\frac{1}{x-5}
derivative of (3x+2^3)	\frac{d}{dx}((3x+2)^{3})
integral from 0 to 1 of 5ln(x)	\int\:_{0}^{1}5\ln(x)dx
taylor f(x)=x*e^{-x+1}	taylor\:f(x)=x\cdot\:e^{-x+1}
integral from 1 to e of 1/(x(x^2+1))	\int\:_{1}^{e}\frac{1}{x(x^{2}+1)}dx
(dy)/(dx)=y+xy^3	\frac{dy}{dx}=y+xy^{3}
derivative of y=2csc(4x^4-2x+5)	derivative\:y=2\csc(4x^{4}-2x+5)
x^{''}+9x=0	x^{\prime\:\prime\:}+9x=0
sum from n=1 to infinity of 1/(1+n^2)	\sum\:_{n=1}^{\infty\:}\frac{1}{1+n^{2}}
(\partial)/(\partial x)(sqrt(2x^3+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{2x^{3}+y^{2}})
d/(dz)(1/(1-z^{-1)})	\frac{d}{dz}(\frac{1}{1-z^{-1}})
d/(dy)(4x^2y^3-4)	\frac{d}{dy}(4\cdot\:x^{2}\cdot\:y^{3}-4)
derivative of y=(t^2-7)^2	derivative\:y=(t^{2}-7)^{2}
(\partial)/(\partial x)(4cos(x))	\frac{\partial\:}{\partial\:x}(4\cos(x))
derivative of 8arcsin(x^4)	\frac{d}{dx}(8\arcsin(x^{4}))
y^'+5y=x	y^{\prime\:}+5y=x
derivative of x^3-3x^2+3	\frac{d}{dx}(x^{3}-3x^{2}+3)
derivative of e^x-x^3-7	\frac{d}{dx}(e^{x}-x^{3}-7)
derivative of 60x^2	\frac{d}{dx}(60x^{2})
integral of e^{cos(x)}	\int\:e^{\cos(x)}dx
integral of (cos(x)+1/6 x)	\int\:(\cos(x)+\frac{1}{6}x)dx
integral of-(x^3)/(sqrt(1-x^2))	\int\:-\frac{x^{3}}{\sqrt{1-x^{2}}}dx
derivative of e^{ax^5}	\frac{d}{dx}(e^{ax^{5}})
limit as x approaches 0 of 2x(1-ln(x))	\lim\:_{x\to\:0}(2x(1-\ln(x)))
derivative of arcsin(x^9)	\frac{d}{dx}(\arcsin(x^{9}))
derivative of f(x)=6x^2-4x	derivative\:f(x)=6x^{2}-4x
(\partial)/(\partial x)(x(5z^4-4y^3))	\frac{\partial\:}{\partial\:x}(x(5z^{4}-4y^{3}))
d/(dt)(4e^tcos(t))	\frac{d}{dt}(4e^{t}\cos(t))
limit as x approaches 0 of (x^3-8)/(x+2)	\lim\:_{x\to\:0}(\frac{x^{3}-8}{x+2})
derivative of f(x)=e-1	derivative\:f(x)=e-1
-y/(x^2)dx+1/x dy=0	-\frac{y}{x^{2}}dx+\frac{1}{x}dy=0
derivative of h(x)=(x-4)(x/2+1)^3	derivative\:h(x)=(x-4)(\frac{x}{2}+1)^{3}
limit as x approaches 3+of (x+1)/(x^2-9)	\lim\:_{x\to\:3+}(\frac{x+1}{x^{2}-9})
integral of (8x-10y+2)	\int\:(8x-10y+2)dy
y^{''}+2y^'+2y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=0
(\partial)/(\partial y)(x/(x^6-y^4))	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{6}-y^{4}})
y^'+y=e^{-t}-1	y^{\prime\:}+y=e^{-t}-1
derivative of 5x^4ln(x+x^4)	\frac{d}{dx}(5x^{4}\ln(x)+x^{4})
area 1/4 (x-3)^2+1,x^2+1,0,3	area\:\frac{1}{4}(x-3)^{2}+1,x^{2}+1,0,3
f(x)=sin^2(5x)	f(x)=\sin^{2}(5x)
(\partial)/(\partial x)(x^3+2xy)	\frac{\partial\:}{\partial\:x}(x^{3}+2xy)
area x^2-4,-4,3	area\:x^{2}-4,-4,3
inverse oflaplace x/((x-1)^2)	inverselaplace\:\frac{x}{(x-1)^{2}}
sum from n=0 to infinity of p^k	\sum\:_{n=0}^{\infty\:}p^{k}
sum from n=1 to infinity of (n-8)/(n+8)	\sum\:_{n=1}^{\infty\:}\frac{n-8}{n+8}
integral of (e^x+a^x)	\int\:(e^{x}+a^{x})dx
integral of 1/((1+sqrt(x)))	\int\:\frac{1}{(1+\sqrt{x})}dx
integral from 0 to pi of sin(2x)cos(x)	\int\:_{0}^{π}\sin(2x)\cos(x)dx
y^{''}-y^'=3x^2e^x	y^{\prime\:\prime\:}-y^{\prime\:}=3x^{2}e^{x}
derivative of (sqrt(1+x)/2)	\frac{d}{dx}(\frac{\sqrt{1+x}}{2})
integral of 1/((x-9)sqrt(x^2-18x))	\int\:\frac{1}{(x-9)\sqrt{x^{2}-18x}}dx
expand 2/((-x^3+9x)^4)	expand\:\frac{2}{(-x^{3}+9x)^{4}}
integral of x/(1+x)	\int\:\frac{x}{1+x}dx
y^'=1+x-y-xy,y(0)=-1	y^{\prime\:}=1+x-y-xy,y(0)=-1
limit as x approaches pi of-4sin(x/2)	\lim\:_{x\to\:π}(-4\sin(\frac{x}{2}))
(1-x^2)y^'=1	(1-x^{2})y^{\prime\:}=1
(\partial)/(\partial x)(25x^8y^4+12x^4y^5)	\frac{\partial\:}{\partial\:x}(25x^{8}y^{4}+12x^{4}y^{5})
integral of 5e^x+cos(x/2)	\int\:5e^{x}+\cos(\frac{x}{2})dx
derivative of 2^{arctan(x)}	derivative\:2^{\arctan(x)}
integral of (2x-3)^2	\int\:(2x-3)^{2}dx
derivative of x^3arctan(3x)	\frac{d}{dx}(x^{3}\arctan(3x))
derivative of 3(sin(x))^x	derivative\:3(\sin(x))^{x}
area x^2-4,x=-4,x=3	area\:x^{2}-4,x=-4,x=3
derivative of 3e	derivative\:3e
derivative of ln(sqrt(x^2-14))	\frac{d}{dx}(\ln(\sqrt{x^{2}-14}))
integral from 1 to 2 of 1/(x^3+4x)	\int\:_{1}^{2}\frac{1}{x^{3}+4x}dx
laplacetransform (5e^{9t}-4)e^{-6t}	laplacetransform\:(5e^{9t}-4)e^{-6t}
laplacetransform (t)^2	laplacetransform\:(t)^{2}
integral of 4/(sqrt(81-(x+9)^2))	\int\:\frac{4}{\sqrt{81-(x+9)^{2}}}dx
y^'+7y=3	y^{\prime\:}+7y=3
integral of (x-4)/(x(x-1)^2)	\int\:\frac{x-4}{x(x-1)^{2}}dx
limit as x approaches 2 of (x-2)/(x-2)	\lim\:_{x\to\:2}(\frac{x-2}{x-2})
derivative of \sqrt[3]{x-9}	\frac{d}{dx}(\sqrt[3]{x-9})
integral of (yze^{xz})	\int\:(yze^{xz})dx
t(dy)/(dt)+3y=9t	t\frac{dy}{dt}+3y=9t
integral of (x+3)sqrt(x)	\int\:(x+3)\sqrt{x}dx
area 7x, 1/x ,x	area\:7x,\frac{1}{x},x
tangent of f(x)=x^4-25x^2+144,\at x=-2	tangent\:f(x)=x^{4}-25x^{2}+144,\at\:x=-2
derivative of sech(ln(x^2))	\frac{d}{dx}(\sech(\ln(x^{2})))
integral from 0 to 1 of arctan(5x+3)	\int\:_{0}^{1}\arctan(5x+3)dx
tangent of f(x)=(2x)/(x+2),(2,1)	tangent\:f(x)=\frac{2x}{x+2},(2,1)
inverse oflaplace 1/(((s+1)^2+4))	inverselaplace\:\frac{1}{((s+1)^{2}+4)}
integral of sin^5(tco)s^4t	\int\:\sin^{5}(tco)s^{4}tdt
derivative of ,xe^y	\frac{d}{dx}(,xe^{y})
tangent of ln(x^2-24)=x-y+6	tangent\:\ln(x^{2}-24)=x-y+6
integral of 4cos^2(31x)	\int\:4\cos^{2}(31x)dx
integral from 1 to 2 of x-sqrt(x)	\int\:_{1}^{2}x-\sqrt{x}dx
(\partial)/(\partial z)(cos(x))	\frac{\partial\:}{\partial\:z}(\cos(x))
d/(du)(sqrt(u^9+v^5))	\frac{d}{du}(\sqrt{u^{9}+v^{5}})
y^'+(x+1)y=e^{x^2}y^3	y^{\prime\:}+(x+1)y=e^{x^{2}}y^{3}

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