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Popular Calculus Problems

sum from n=1 to infinity of (3^n)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{n!}
limit as (x,y) approaches (3,2) of e^{sqrt(2x-y)}	\lim\:_{(x,y)\to\:(3,2)}(e^{\sqrt{2x-y}})
integral of xinx	\int\:xinxdx
integral of (x+3)^{3/2}	\int\:(x+3)^{\frac{3}{2}}dx
slope of (-4,1),(1,-2)	slope\:(-4,1),(1,-2)
derivative of cos(3x^2+3x)	\frac{d}{dx}(\cos(3x^{2}+3x))
integral of (3x^2-1)e^x	\int\:(3x^{2}-1)e^{x}dx
integral of csc((ax)/b)cot((ax)/b)	\int\:\csc(\frac{ax}{b})\cot(\frac{ax}{b})dx
derivative of 4e^0	\frac{d}{dx}(4e^{0})
taylor sin(x/2),pi	taylor\:\sin(\frac{x}{2}),π
derivative of 1/(x^2-1)	derivative\:\frac{1}{x^{2}-1}
integral of e^1	\int\:e^{1}dx
derivative of arctan(sqrt((1+x)/(1-x)))	derivative\:\arctan(\sqrt{\frac{1+x}{1-x}})
y^{''}-3y^'+2y=2e^t	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=2e^{t}
integral of cos(a)x	\int\:\cos(a)xdx
derivative of xe^y	derivative\:xe^{y}
integral of (sqrt(9-x^2))	\int\:(\sqrt{9-x^{2}})dx
area ((x^2))/2 ,x+4	area\:\frac{(x^{2})}{2},x+4
derivative of f(θ)=sin(θ)cos(θ)	derivative\:f(θ)=\sin(θ)\cos(θ)
integral of tan(10x)	\int\:\tan(10x)dx
limit as x approaches infinity of x-1/x	\lim\:_{x\to\:\infty\:}(x-\frac{1}{x})
integral from 1 to infinity of 6/(x^3)	\int\:_{1}^{\infty\:}\frac{6}{x^{3}}dx
(\partial)/(\partial x)(1.2)	\frac{\partial\:}{\partial\:x}(1.2)
y^'=1+x+y+xy	y^{\prime\:}=1+x+y+xy
integral from 6 to 8 of (42)/((x-6)^3)	\int\:_{6}^{8}\frac{42}{(x-6)^{3}}dx
integral of x^2e^{x^3}	\int\:x^{2}e^{x^{3}}dx
slope of (0.1)(3)	slope\:(0.1)(3)
(\partial)/(\partial x)(cos(2x))	\frac{\partial\:}{\partial\:x}(\cos(2x))
derivative of 1/x+1	\frac{d}{dx}(\frac{1}{x}+1)
integral from 6 to 10 of 2/(x^3)	\int\:_{6}^{10}\frac{2}{x^{3}}dx
integral of 3/((2-x)^2)	\int\:\frac{3}{(2-x)^{2}}dx
integral of 1/(2+2x+x^2)	\int\:\frac{1}{2+2x+x^{2}}dx
derivative of e^{-xln(2x})	\frac{d}{dx}(e^{-x\ln(2x)})
derivative of (-x+2/(x^3))	\frac{d}{dx}(\frac{-x+2}{x^{3}})
derivative of cos^4(3x)	\frac{d}{dx}(\cos^{4}(3x))
x^2(dy)/(dx)+2xy=y^3	x^{2}\frac{dy}{dx}+2xy=y^{3}
integral of sqrt(2+7x)	\int\:\sqrt{2+7x}dx
integral of (121)/(x^3-11x^2)	\int\:\frac{121}{x^{3}-11x^{2}}dx
derivative of f(x)=sqrt(7x+4)	derivative\:f(x)=\sqrt{7x+4}
derivative of (xy+1^2)	\frac{d}{dx}((xy+1)^{2})
limit as x approaches 2 of x^2-sqrt(x+2)	\lim\:_{x\to\:2}(x^{2}-\sqrt{x+2})
integral of (2^{ln(x)})/x	\int\:\frac{2^{\ln(x)}}{x}dx
integral of x^3cos(x)	\int\:x^{3}\cos(x)dx
integral from-2 to-1 of (2x^2)-(2x+6)	\int\:_{-2}^{-1}(2x^{2})-(2x+6)dx
(\partial)/(\partial x)(x^6e^{xy})	\frac{\partial\:}{\partial\:x}(x^{6}e^{xy})
(d^2)/(dx^2)((4x^2+9)^6)	\frac{d^{2}}{dx^{2}}((4x^{2}+9)^{6})
derivative of (x^2/2)	\frac{d}{dx}(\frac{x^{2}}{2})
(\partial)/(\partial x)(e^x+xcos(y))	\frac{\partial\:}{\partial\:x}(e^{x}+x\cos(y))
integral of (x^2-1)/(e^{x/2)}	\int\:\frac{x^{2}-1}{e^{\frac{x}{2}}}dx
derivative of 3^{x-inx}	\frac{d}{dx}(3^{x-inx})
integral of (x^2)/(49+x^2)	\int\:\frac{x^{2}}{49+x^{2}}dx
limit as x approaches 0 of 2x	\lim\:_{x\to\:0}(2x)
derivative of 1000e^{-0.02p}	derivative\:1000e^{-0.02p}
integral of 2x^2cos((npix)/2)	\int\:2x^{2}\cos(\frac{nπx}{2})dx
derivative of sqrt(x)ln(x)	derivative\:\sqrt{x}\ln(x)
limit as x approaches+2 of ((x^2-2x))/((x^2-4x+4))	\lim\:_{x\to\:+2}(\frac{(x^{2}-2x)}{(x^{2}-4x+4)})
derivative of x^2y	derivative\:x^{2}y
d/(dt)(2sin(2t))	\frac{d}{dt}(2\sin(2t))
derivative of (3x+1)/(x^2+1)	derivative\:\frac{3x+1}{x^{2}+1}
y^'=x+y,y(0)=1	y^{\prime\:}=x+y,y(0)=1
derivative of 3(2ze^z+e^zz^2)	derivative\:3(2ze^{z}+e^{z}z^{2})
derivative of f(x)=(x-4)^2	derivative\:f(x)=(x-4)^{2}
tangent of 9+5x^2	tangent\:9+5x^{2}
integral from 0 to R of 1/(1+x^2)	\int\:_{0}^{R}\frac{1}{1+x^{2}}dx
integral of ((sqrt(x)-b))/(sqrt(x))	\int\:\frac{(\sqrt{x}-b)}{\sqrt{x}}dx
(\partial)/(\partial x)(sin(x)e^{yx^2}x)	\frac{\partial\:}{\partial\:x}(\sin(x)e^{yx^{2}}x)
integral of z/(sqrt(1+z^2))	\int\:\frac{z}{\sqrt{1+z^{2}}}dz
integral of e^{x^2-2x}	\int\:e^{x^{2}-2x}dx
derivative of x^{1/2}*csc(xsin(x))	\frac{d}{dx}(x^{\frac{1}{2}}\cdot\:\csc(x)\sin(x))
2y^'-6x^2=0	2y^{\prime\:}-6x^{2}=0
(\partial)/(\partial x)(ysin(x))	\frac{\partial\:}{\partial\:x}(y\sin(x))
integral from 0 to 3 of (5t-8)	\int\:_{0}^{3}(5t-8)dt
derivative of e^{2x^2}	derivative\:e^{2x^{2}}
integral of-xe^{(x^2)/2}	\int\:-xe^{\frac{x^{2}}{2}}dx
limit as x approaches 6 of x-6	\lim\:_{x\to\:6}(x-6)
derivative of y=3x^{2/3}	derivative\:y=3x^{\frac{2}{3}}
(\partial)/(\partial y)((5x^3y+4y^5)^3)	\frac{\partial\:}{\partial\:y}((5x^{3}y+4y^{5})^{3})
derivative of x^2+3x-2	derivative\:x^{2}+3x-2
integral from-pi to pi of cos(3x)sin(3x)	\int\:_{-π}^{π}\cos(3x)\sin(3x)dx
limit as x approaches 0 of k/(x(x+1))	\lim\:_{x\to\:0}(\frac{k}{x(x+1)})
limit as x approaches 3+of (x+1)/(3-x)	\lim\:_{x\to\:3+}(\frac{x+1}{3-x})
derivative of y=2sqrt(x)	derivative\:y=2\sqrt{x}
derivative of 2/5 x^3cos(x)	\frac{d}{dx}(\frac{2}{5}x^{3}\cos(x))
derivative of ln(x^2y)	\frac{d}{dx}(\ln(x^{2}y))
derivative of (6x^2+8x+8/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+8x+8}{\sqrt{x}})
derivative of 84x^6+12x^3-24x^2	\frac{d}{dx}(84x^{6}+12x^{3}-24x^{2})
integral of (1-2x)^4	\int\:(1-2x)^{4}dx
integral of 1/((4+9x^2))	\int\:\frac{1}{(4+9x^{2})}dx
x^2y^{''}+3xy^'-4y=0	x^{2}y^{\prime\:\prime\:}+3xy^{\prime\:}-4y=0
integral of ((x^2+x-6))/((x^2-4x+3))	\int\:\frac{(x^{2}+x-6)}{(x^{2}-4x+3)}dx
tangent of f(x)=((x+1)/(x-1))^3,\at x=2	tangent\:f(x)=(\frac{x+1}{x-1})^{3},\at\:x=2
integral of 6x^2e^{x^3}	\int\:6x^{2}e^{x^{3}}dx
integral of 1/(3-2x-x^2)	\int\:\frac{1}{3-2x-x^{2}}dx
(\partial)/(\partial x)(xye^{yz})	\frac{\partial\:}{\partial\:x}(xye^{yz})
integral from-1 to 5 of \|2x-3\|	\int\:_{-1}^{5}\left\|2x-3\right\|dx
inverse oflaplace-(2s+1)/(s^2+3s+2)	inverselaplace\:-\frac{2s+1}{s^{2}+3s+2}
(\partial)/(\partial y)(x^3y^6)	\frac{\partial\:}{\partial\:y}(x^{3}y^{6})
integral of (3x^{-2}-4x^2+1)	\int\:(3x^{-2}-4x^{2}+1)dx
(\partial)/(\partial x)(e^{-9x}cos(θ))	\frac{\partial\:}{\partial\:x}(e^{-9x}\cos(θ))
inverse oflaplace s/(s^2+4^2)	inverselaplace\:\frac{s}{s^{2}+4^{2}}

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