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Popular Calculus Problems

integral of (x^2)/(x^2+x+56)	\int\:\frac{x^{2}}{x^{2}+x+56}dx
parity f(x)=(sin(3x))^{3x}	parity\:f(x)=(\sin(3x))^{3x}
integral of e^{6x}sin(e^{3x})	\int\:e^{6x}\sin(e^{3x})dx
derivative of 2x-x^2	\frac{d}{dx}(2x-x^{2})
integral of e^xsqrt(25+e^x)	\int\:e^{x}\sqrt{25+e^{x}}dx
(dy)/(dx)=(x^2+y^2)/(2xy)	\frac{dy}{dx}=\frac{x^{2}+y^{2}}{2xy}
derivative of cot(x-sin(2x))	\frac{d}{dx}(\cot(x)-\sin(2x))
area y=x,x^2,[0,1]	area\:y=x,x^{2},[0,1]
tangent of y=-(8x)/(x^2+1),(1,-4)	tangent\:y=-\frac{8x}{x^{2}+1},(1,-4)
area x^2+2x+11,-4x+2,x=0	area\:x^{2}+2x+11,-4x+2,x=0
limit as x approaches 6 of \|x-6\|	\lim\:_{x\to\:6}(\left\|x-6\right\|)
y^{''}-3y^'+2y=e^t+e^{2t}	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{t}+e^{2t}
area y=x,y=2x,y=-x+2	area\:y=x,y=2x,y=-x+2
derivative of 72x^2	\frac{d}{dx}(72x^{2})
y^{''}+3y^'+2y=x	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=x
tangent of f(x)=5x^2-8x,\at x=1	tangent\:f(x)=5x^{2}-8x,\at\:x=1
limit as x approaches 2 of ax+b	\lim\:_{x\to\:2}(ax+b)
derivative of (2x^2)/(x^2-1)	derivative\:\frac{2x^{2}}{x^{2}-1}
derivative of (e^x/(8x^2))	\frac{d}{dx}(\frac{e^{x}}{8x^{2}})
derivative of (6x-1)/(2x+9)	derivative\:\frac{6x-1}{2x+9}
integral of e^{-z^2}	\int\:e^{-z^{2}}dz
integral of x/(sqrt(x^2+4))	\int\:\frac{x}{\sqrt{x^{2}+4}}dx
limit as x approaches 2 of-1/((x-2)^2)	\lim\:_{x\to\:2}(-\frac{1}{(x-2)^{2}})
tangent of y=sqrt(x^2-x+7),\at x=7	tangent\:y=\sqrt{x^{2}-x+7},\at\:x=7
limit as x approaches 1 of (x^9-1)/(x-1)	\lim\:_{x\to\:1}(\frac{x^{9}-1}{x-1})
derivative of tan(1/2 x)	\frac{d}{dx}(\tan(\frac{1}{2}x))
integral of sin(x+3)	\int\:\sin(x+3)dx
(\partial)/(\partial x)(3x^2+2y^2-4xy+5)	\frac{\partial\:}{\partial\:x}(3x^{2}+2y^{2}-4xy+5)
d/(dt)(t/(1+(1.5574+5.43t^2)^2))	\frac{d}{dt}(\frac{t}{1+(1.5574+5.43t^{2})^{2}})
derivative of (x^3-2x(x^{-4}+x^{-2}))	\frac{d}{dx}((x^{3}-2x)(x^{-4}+x^{-2}))
y^'=0.0014y(1600-y)	y^{\prime\:}=0.0014y(1600-y)
(\partial)/(\partial x)(3x^2y^3)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{3})
integral of 3-4x	\int\:3-4xdx
derivative of 1+2/x	\frac{d}{dx}(1+\frac{2}{x})
sum from n=1 to infinity of 5(0.8)^{n-1}	\sum\:_{n=1}^{\infty\:}5(0.8)^{n-1}
y^{''}+6y^'=0	y^{\prime\:\prime\:}+6y^{\prime\:}=0
integral from 2 to infinity of ye^{-3y}	\int\:_{2}^{\infty\:}ye^{-3y}dy
limit as x approaches-2-of-2x+6	\lim\:_{x\to\:-2-}(-2x+6)
integral from 0 to 1 of (55)/(4y-1)	\int\:_{0}^{1}\frac{55}{4y-1}dy
derivative of y=log_{3}(6x)	derivative\:y=\log_{3}(6x)
(\partial)/(\partial z)(y^{xz}+2(yz)^x)	\frac{\partial\:}{\partial\:z}(y^{xz}+2(yz)^{x})
integral of 5e^{-3x}(4-e^{-3x})^5	\int\:5e^{-3x}(4-e^{-3x})^{5}dx
derivative of (4x^3+5(x^4-2x))	\frac{d}{dx}((4x^{3}+5)(x^{4}-2x))
limit as x approaches 3 of (\|x\|)/x	\lim\:_{x\to\:3}(\frac{\left\|x\right\|}{x})
integral from 0 to (3pi)/2 of cos^3(41x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(41x)dx
inverse oflaplace s/((s^2+25)(s^2+16))	inverselaplace\:\frac{s}{(s^{2}+25)(s^{2}+16)}
integral of x^2(4x^3-3)^4	\int\:x^{2}(4x^{3}-3)^{4}dx
integral of-6sec^2(x)	\int\:-6\sec^{2}(x)dx
f(x)=2xln(x)+x^2-1	f(x)=2x\ln(x)+x^{2}-1
integral of 5e^xsin^2(x)	\int\:5e^{x}\sin^{2}(x)dx
integral of 9cot^3(x)csc^3(x)	\int\:9\cot^{3}(x)\csc^{3}(x)dx
derivative of 6e^x+4ln(x)	derivative\:6e^{x}+4\ln(x)
y^'-6/x y=(y^4)/(x^{12)}	y^{\prime\:}-\frac{6}{x}y=\frac{y^{4}}{x^{12}}
integral of (4ln(4x^4))/(x^4)	\int\:\frac{4\ln(4x^{4})}{x^{4}}dx
derivative of (4x/(2x^2+1))	\frac{d}{dx}(\frac{4x}{2x^{2}+1})
derivative of (x+2)^2+(10-3x)^2	derivative\:(x+2)^{2}+(10-3x)^{2}
limit as x approaches-1-of (x^2)/(x+1)	\lim\:_{x\to\:-1-}(\frac{x^{2}}{x+1})
slope of (1,0),(0,1)	slope\:(1,0),(0,1)
derivative of (sqrt(2x-5)/x)	\frac{d}{dx}(\frac{\sqrt{2x-5}}{x})
integral of x^2-6x-27	\int\:x^{2}-6x-27dx
4x(dy)/(dx)=sqrt(x^2-9)	4x\frac{dy}{dx}=\sqrt{x^{2}-9}
integral from-1 to 1 of ln(ln(x+3))	\int\:_{-1}^{1}\ln(\ln(x+3))dx
(dx)/(dy)=-((4y^2+6xy))/(3y^2+2x)	\frac{dx}{dy}=-\frac{(4y^{2}+6xy)}{3y^{2}+2x}
integral from 0 to 2 of (6x^2-4x+5)	\int\:_{0}^{2}(6x^{2}-4x+5)dx
derivative of y=e^{1/2 x}	derivative\:y=e^{\frac{1}{2}x}
limit as x approaches a of (f(x))/(p(x))	\lim\:_{x\to\:a}(\frac{f(x)}{p(x)})
area y=3-x,y=2x^2,0,1	area\:y=3-x,y=2x^{2},0,1
integral of 1+2y	\int\:1+2ydy
limit as x approaches 1 of sin(-3pix)	\lim\:_{x\to\:1}(\sin(-3πx))
(\partial)/(\partial y)((xy)/(x-y))	\frac{\partial\:}{\partial\:y}(\frac{xy}{x-y})
derivative of x^2-4/(x^3)	\frac{d}{dx}(x^{2}-\frac{4}{x^{3}})
derivative of (8x^2+4x+2/(sqrt(x)))	\frac{d}{dx}(\frac{8x^{2}+4x+2}{\sqrt{x}})
integral from 1 to infinity of x/(e^x)	\int\:_{1}^{\infty\:}\frac{x}{e^{x}}dx
(\partial)/(\partial x)(60x^{4/5}y^{1/5})	\frac{\partial\:}{\partial\:x}(60x^{\frac{4}{5}}y^{\frac{1}{5}})
integral of x/(sqrt(4-9x^2))	\int\:\frac{x}{\sqrt{4-9x^{2}}}dx
integral of 2cos((npix)/2)	\int\:2\cos(\frac{nπx}{2})dx
integral of (2x)/((x^2-1)^2)	\int\:\frac{2x}{(x^{2}-1)^{2}}dx
(dy)/(dx)=3^{e^{2x}}y^2	\frac{dy}{dx}=3^{e^{2x}}y^{2}
derivative of 9/(8x^4)	derivative\:\frac{9}{8x^{4}}
limit as x approaches 1 of 8/(sqrt(1-x))	\lim\:_{x\to\:1}(\frac{8}{\sqrt{1-x}})
2x^{''}+4x^'+8x=0	2x^{\prime\:\prime\:}+4x^{\prime\:}+8x=0
derivative of 3/(x^2-5)	\frac{d}{dx}(\frac{3}{x^{2}-5})
tangent of f(x)=8x-x^2,(1,7)	tangent\:f(x)=8x-x^{2},(1,7)
sum from k=0 to infinity of sin(k)	\sum\:_{k=0}^{\infty\:}\sin(k)
derivative of 2^{40}	derivative\:2^{40}
6(dy)/(dx)=y^2	6\frac{dy}{dx}=y^{2}
sum from n=1 to infinity of ln(*1/n)	\sum\:_{n=1}^{\infty\:}\ln(\cdot\:\frac{1}{n})
derivative of e^{ktan(sqrt(5x)})	\frac{d}{dx}(e^{k\tan(\sqrt{5x})})
integral of 2cos(3x)	\int\:2\cos(3x)dx
derivative of f(x)=26x+ln(26x)	derivative\:f(x)=26x+\ln(26x)
derivative of 500(1+x/(1200)^{120})	\frac{d}{dx}(500(1+\frac{x}{1200})^{120})
derivative of f(x)=(3x^2)/(sqrt(2))	derivative\:f(x)=\frac{3x^{2}}{\sqrt{2}}
limit as x approaches 0 of xn(x)	\lim\:_{x\to\:0}(xn(x))
integral of x^2e^{-x/a}	\int\:x^{2}e^{-\frac{x}{a}}dx
integral of (cos(y)cos(z))	\int\:(\cos(y)\cos(z))dy
derivative of 5+2x^2	\frac{d}{dx}(5+2x^{2})
area x^2-2x+2,g(3)=2x-2,[0,3]	area\:x^{2}-2x+2,g(3)=2x-2,[0,3]
derivative of b^2	derivative\:b^{2}
derivative of 1/(x^2+1)	derivative\:\frac{1}{x^{2}+1}
limit as x approaches 0-of arctan(1/x)+pi	\lim\:_{x\to\:0-}(\arctan(\frac{1}{x})+π)

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