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Popular Calculus Problems

limit as x approaches-6-of (-1)/(x+6)	\lim\:_{x\to\:-6-}(\frac{-1}{x+6})
laplacetransform x-1	laplacetransform\:x-1
integral of e^{x^3}x^2	\int\:e^{x^{3}}x^{2}dx
integral from 0 to 1 of (x^2-4x+5)	\int\:_{0}^{1}(x^{2}-4x+5)dx
sum from n=1 to infinity of 2^{-3n}	\sum\:_{n=1}^{\infty\:}2^{-3n}
d/(dy)(9xe^{-1/(y^3)})	\frac{d}{dy}(9xe^{-\frac{1}{y^{3}}})
integral of e^{x^2+3}	\int\:e^{x^{2}+3}dx
slope of y=8x-x^2,(1,7)	slope\:y=8x-x^{2},(1,7)
y^{''}-2y^'-8y=0\quad y(0)=-2,y^'(0)=4	y^{\prime\:\prime\:}-2y^{\prime\:}-8y=0\quad\:y(0)=-2,y^{\prime\:}(0)=4
integral of (t+2t^2)/(sqrt(t))	\int\:\frac{t+2t^{2}}{\sqrt{t}}dt
(xdy)/(dx)=4y	\frac{xdy}{dx}=4y
sum from n=1 to infinity of 1/(1+ln(n))	\sum\:_{n=1}^{\infty\:}\frac{1}{1+\ln(n)}
(\partial)/(\partial x)(3x^4y)	\frac{\partial\:}{\partial\:x}(3x^{4}y)
derivative of (4x^4-7x/(x^3-8))	\frac{d}{dx}(\frac{4x^{4}-7x}{x^{3}-8})
tangent of f(x)=2x^2-9x+10,\at x=3	tangent\:f(x)=2x^{2}-9x+10,\at\:x=3
derivative of x^4+x^2	\frac{d}{dx}(x^{4}+x^{2})
derivative of e^{(6x-7x^2})	\frac{d}{dx}(e^{(6x-7x^{2})})
integral from-2 to 2 of e^{-x^2}	\int\:_{-2}^{2}e^{-x^{2}}dx
tangent of y=2x-2x^2	tangent\:y=2x-2x^{2}
limit as x approaches 2 of 1/2 x^2-4x	\lim\:_{x\to\:2}(\frac{1}{2}x^{2}-4x)
derivative of 2e^{2t}	derivative\:2e^{2t}
area x=-2,x=3,y=2x^2+2,y=0	area\:x=-2,x=3,y=2x^{2}+2,y=0
tangent of 2x^2+x-1,\at x=-1	tangent\:2x^{2}+x-1,\at\:x=-1
integral of cot^5(x)sin^4(x)	\int\:\cot^{5}(x)\sin^{4}(x)dx
implicit (dy)/(dx),cos(x+y)=sin(x)sin(y)	implicit\:\frac{dy}{dx},\cos(x+y)=\sin(x)\sin(y)
derivative of e^2x	\frac{d}{dx}(e^{2}x)
tangent of Y(x)=x^2+3	tangent\:Y(x)=x^{2}+3
derivative of (t^2+7)/((6t-2)^6)	derivative\:\frac{t^{2}+7}{(6t-2)^{6}}
limit as x approaches 6-of cx^2+9x	\lim\:_{x\to\:6-}(cx^{2}+9x)
integral of sin((nxpi)/2)	\int\:\sin(\frac{nxπ}{2})dx
y^{''}+3y^'+2y=cos(e^x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\cos(e^{x})
integral of 1/(x^2)ln(3x)	\int\:\frac{1}{x^{2}}\ln(3x)dx
implicit (dy)/(dx),y=xe^y	implicit\:\frac{dy}{dx},y=xe^{y}
limit as x approaches 6-of sec((pix)/4)	\lim\:_{x\to\:6-}(\sec(\frac{πx}{4}))
(\partial)/(\partial y)(2x-3y)	\frac{\partial\:}{\partial\:y}(2x-3y)
(\partial)/(\partial y)(1/(xy))	\frac{\partial\:}{\partial\:y}(\frac{1}{xy})
y^'=(15x)/y	y^{\prime\:}=\frac{15x}{y}
integral of e^{x(t-1)}	\int\:e^{x(t-1)}dx
(\partial)/(\partial x)(arctan(x))	\frac{\partial\:}{\partial\:x}(\arctan(x))
inverse oflaplace 1/(s^2+s(3/2)2)	inverselaplace\:\frac{1}{s^{2}+s(\frac{3}{2})2}
integral of 1/(sqrt(7x))	\int\:\frac{1}{\sqrt{7x}}dx
integral of (x^2)/(x^2+x-2)	\int\:\frac{x^{2}}{x^{2}+x-2}dx
integral of (5x^3-3x^2+2x-1)/(x^4+x^2)	\int\:\frac{5x^{3}-3x^{2}+2x-1}{x^{4}+x^{2}}dx
integral of 3x^2e^{(x^3)}	\int\:3x^{2}e^{(x^{3})}dx
derivative of (x^2-6x+12/(x-4))	\frac{d}{dx}(\frac{x^{2}-6x+12}{x-4})
integral of 24x^2	\int\:24x^{2}dx
integral of x/(sqrt(x^2+4x+5))	\int\:\frac{x}{\sqrt{x^{2}+4x+5}}dx
derivative of (e^x+4^3)	\frac{d}{dx}((e^{x}+4)^{3})
integral of x^2+5x+6	\int\:x^{2}+5x+6dx
2sin(x),3cos(x),x=0,x=0.7pi	2\sin(x),3\cos(x),x=0,x=0.7π
integral of (\sqrt[11]{x}+\sqrt[12]{x})	\int\:(\sqrt[11]{x}+\sqrt[12]{x})dx
integral of xe^{-inx}	\int\:xe^{-inx}dx
integral of (sec(x)tan(x))/(9+4sec^2(x))	\int\:\frac{\sec(x)\tan(x)}{9+4\sec^{2}(x)}dx
integral of cos(t)e^t	\int\:\cos(t)e^{t}dt
(dx)/(dy)=y^2x-x+y^2-1	\frac{dx}{dy}=y^{2}x-x+y^{2}-1
integral of tan^2(x)sec^3(x	\int\:\tan^{2}(x)\sec^{3}(d)xdx
maclaurin f(x)=arctan(x)	maclaurin\:f(x)=\arctan(x)
integral of (e^{2x})/(sqrt(e^x+1))	\int\:\frac{e^{2x}}{\sqrt{e^{x}+1}}dx
integral from 0 to 1 of 3ln(6x)	\int\:_{0}^{1}3\ln(6x)dx
integral of x^2-3x+4	\int\:x^{2}-3x+4dx
limit as x approaches 0+of sin(x)ln(7x)	\lim\:_{x\to\:0+}(\sin(x)\ln(7x))
limit as x approaches 2+of ((x-3))/(x-2)	\lim\:_{x\to\:2+}(\frac{(x-3)}{x-2})
integral of (e^x-4e^{-x})/(e^x)	\int\:\frac{e^{x}-4e^{-x}}{e^{x}}dx
y^3-(10x+2)+3xy^2(dy)/(dx)=0	y^{3}-(10x+2)+3xy^{2}\frac{dy}{dx}=0
(\partial)/(\partial x)(xe^y+y+1)	\frac{\partial\:}{\partial\:x}(xe^{y}+y+1)
(\partial}{\partial y}(\frac{x^2-y^2)/2)	\frac{\partial\:}{\partial\:y}(\frac{x^{2}-y^{2}}{2})
integral from 0 to 0.02 of 200x	\int\:_{0}^{0.02}200xdx
inverse oflaplace (3s+1)/(s(s+2))	inverselaplace\:\frac{3s+1}{s(s+2)}
tangent of 1/(2x+2),\at x=5	tangent\:\frac{1}{2x+2},\at\:x=5
(4-x^2)(dy)/(dx)=2y	(4-x^{2})\frac{dy}{dx}=2y
tangent of y=((x+1)/(x-3))^2,(7,4)	tangent\:y=(\frac{x+1}{x-3})^{2},(7,4)
integral of 2cos^2(x/2)	\int\:2\cos^{2}(\frac{x}{2})dx
integral of 1/(tln(t))	\int\:\frac{1}{t\ln(t)}dt
tangent of y=5e^x+x,(0,5)	tangent\:y=5e^{x}+x,(0,5)
integral of 1/(49-64x^2)	\int\:\frac{1}{49-64x^{2}}dx
integral of t^7e^{-t^4}	\int\:t^{7}e^{-t^{4}}dt
derivative of f(x)=(x+9)/(sqrt(x))	derivative\:f(x)=\frac{x+9}{\sqrt{x}}
derivative of (3x^4+3/(sin(x)))	\frac{d}{dx}(\frac{3x^{4}+3}{\sin(x)})
d/(ds)(sqrt(s^2+t^2))	\frac{d}{ds}(\sqrt{s^{2}+t^{2}})
tangent of 3x^4-7x^2,\at x=-1	tangent\:3x^{4}-7x^{2},\at\:x=-1
integral of (-2x+4)/((x^2+1)(x-1)^2)	\int\:\frac{-2x+4}{(x^{2}+1)(x-1)^{2}}dx
(dy)/(dx)=4y^2sec^2(2x),y(pi/8)=1	\frac{dy}{dx}=4y^{2}\sec^{2}(2x),y(\frac{π}{8})=1
limit as x approaches-3 of 1/2-x^3	\lim\:_{x\to\:-3}(\frac{1}{2}-x^{3})
integral of-tan(3x)	\int\:-\tan(3x)dx
derivative of 2x^3+3x^2-120x	\frac{d}{dx}(2x^{3}+3x^{2}-120x)
(dv)/(dy)=(v-y^3)/(v-y)	\frac{dv}{dy}=\frac{v-y^{3}}{v-y}
derivative of f(x)=sqrt(25-x^2)	derivative\:f(x)=\sqrt{25-x^{2}}
x(4x+2y)y^'+y(12x+2y)=0	x(4x+2y)y^{\prime\:}+y(12x+2y)=0
integral from-1 to 1 of e^y-y^2-2	\int\:_{-1}^{1}e^{y}-y^{2}-2dy
tangent of y=x^4+3x^3-2x-2	tangent\:y=x^{4}+3x^{3}-2x-2
derivative of log_{5}(sqrt(x^2-1))	derivative\:\log_{5}(\sqrt{x^{2}-1})
limit as x approaches 1 of-x^2-1	\lim\:_{x\to\:1}(-x^{2}-1)
integral of (4x+1)^{-1/2}	\int\:(4x+1)^{-\frac{1}{2}}dx
integral of 20xe^{8x}	\int\:20xe^{8x}dx
(dy)/(dt)= y/(t+1)+4t^2+4t	\frac{dy}{dt}=\frac{y}{t+1}+4t^{2}+4t
derivative of (2x^2/3-sin(x)+3)	\frac{d}{dx}(\frac{2x^{2}}{3}-\sin(x)+3)
limit as x approaches 2 of (x-3)/(x^2+1)	\lim\:_{x\to\:2}(\frac{x-3}{x^{2}+1})
integral of sin^2(xco)s^5x	\int\:\sin^{2}(xco)s^{5}xdx
integral of ax(x-4)	\int\:ax(x-4)dx
integral of xln(2)	\int\:x\ln(2)dx

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