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Popular Calculus Problems

sum from n=3 to infinity of 1/(n(n-1))	\sum\:_{n=3}^{\infty\:}\frac{1}{n(n-1)}
derivative of sin^3(3x+2)	\frac{d}{dx}(\sin^{3}(3x+2))
taylor (-x+ln(1+x))/(x^2)	taylor\:\frac{-x+\ln(1+x)}{x^{2}}
integral of 1/(sqrt(x)\sqrt{1-x)}	\int\:\frac{1}{\sqrt{x}\sqrt{1-x}}dx
derivative of x^6(5.1)^x	derivative\:x^{6}(5.1)^{x}
limit as x approaches 0 of (1/(x^2))^x	\lim\:_{x\to\:0}((\frac{1}{x^{2}})^{x})
integral of 7+7tan^2(x)	\int\:7+7\tan^{2}(x)dx
derivative of (3cos(x)/(1-sin(x)))	\frac{d}{dx}(\frac{3\cos(x)}{1-\sin(x)})
integral of (x^3-x^2+2)/(x^3-2x^2+2x)	\int\:\frac{x^{3}-x^{2}+2}{x^{3}-2x^{2}+2x}dx
integral from 5 to 10 of 8/(5-2x)	\int\:_{5}^{10}\frac{8}{5-2x}dx
derivative of y= 1/3 (x^2+2)^{3/2}	derivative\:y=\frac{1}{3}(x^{2}+2)^{\frac{3}{2}}
derivative of sec(9x)	derivative\:\sec(9x)
derivative of 4.5x+2.4x^2+1.1x^3	\frac{d}{dx}(4.5x+2.4x^{2}+1.1x^{3})
derivative of ln(sqrt(xy))	\frac{d}{dx}(\ln(\sqrt{xy}))
d/(dw)((ln(w))^{(2w)})	\frac{d}{dw}((\ln(w))^{(2w)})
integral from 0 to pi of 4*sin(x)	\int\:_{0}^{π}4\cdot\:\sin(x)dx
integral of 1/((1+2x)^2)	\int\:\frac{1}{(1+2x)^{2}}dx
integral of 1+e^{x^2}	\int\:1+e^{x^{2}}dx
(\partial)/(\partial y)(e^{x^2+y^2}*2y)	\frac{\partial\:}{\partial\:y}(e^{x^{2}+y^{2}}\cdot\:2y)
integral of (x^{1/3}-3)/(x^{2/3)}	\int\:\frac{x^{\frac{1}{3}}-3}{x^{\frac{2}{3}}}dx
integral from 0 to 2 of sqrt(1+4x^2)	\int\:_{0}^{2}\sqrt{1+4x^{2}}dx
q^'+q/(20+t)=1,q(0)=5	q^{\prime\:}+\frac{q}{20+t}=1,q(0)=5
derivative of x^8(x-3)^7	derivative\:x^{8}(x-3)^{7}
sum from n=0 to infinity of 5/(4^{n+1)}	\sum\:_{n=0}^{\infty\:}\frac{5}{4^{n+1}}
limit as x approaches o of (sin(4x))/x	\lim\:_{x\to\:o}(\frac{\sin(4x)}{x})
f^'(x)= 1/(sqrt(x))	f^{\prime\:}(x)=\frac{1}{\sqrt{x}}
f(x)=sqrt(1+3x)	f(x)=\sqrt{1+3x}
y^{''}-9y=e^{-t}+1	y^{\prime\:\prime\:}-9y=e^{-t}+1
integral of (sec^2(x)-tan^2(x))	\int\:(\sec^{2}(x)-\tan^{2}(x))dx
integral from-7 to 7 of (sqrt(49-x^2))	\int\:_{-7}^{7}(\sqrt{49-x^{2}})dx
integral of-2x	\int\:-2xdx
derivative of (40/(0.01x^2+1))	\frac{d}{dx}(\frac{40}{0.01x^{2}+1})
derivative of e^{nx^2}	\frac{d}{dx}(e^{nx^{2}})
x^'=x^2+x	x^{\prime\:}=x^{2}+x
derivative of log_{7}(e^{-x}cos(pix))	\frac{d}{dx}(\log_{7}(e^{-x}\cos(πx)))
tangent of y= 1/(x+1),(1, 1/2)	tangent\:y=\frac{1}{x+1},(1,\frac{1}{2})
laplacetransform (1+t)^3	laplacetransform\:(1+t)^{3}
integral of sqrt(2e^{2t)}	\int\:\sqrt{2e^{2t}}dt
derivative of (x^2+2x^4(x^2+3x^2+7)^3)	\frac{d}{dx}((x^{2}+2x)^{4}(x^{2}+3x^{2}+7)^{3})
tangent of y=x^2-5x+3,(2,-3)	tangent\:y=x^{2}-5x+3,(2,-3)
integral of x*sqrt(x^2-1)	\int\:x\cdot\:\sqrt{x^{2}-1}dx
integral of (sqrt(225-x^2))/x	\int\:\frac{\sqrt{225-x^{2}}}{x}dx
integral of ((1+x)/(sqrt(x)))^2	\int\:(\frac{1+x}{\sqrt{x}})^{2}dx
(\partial)/(\partial x)(sin(x+e^y))	\frac{\partial\:}{\partial\:x}(\sin(x+e^{y}))
8x-6ysqrt(x^2+1)(dy)/(dx)=0	8x-6y\sqrt{x^{2}+1}\frac{dy}{dx}=0
integral of (5-3x)^7	\int\:(5-3x)^{7}dx
integral of 2x^{-5}	\int\:2x^{-5}dx
(\partial)/(\partial y)(5y-e^{8sin(x)})	\frac{\partial\:}{\partial\:y}(5y-e^{8\sin(x)})
sum from n=6 to infinity of 1/(n^2-4)	\sum\:_{n=6}^{\infty\:}\frac{1}{n^{2}-4}
sum from n=1 to infinity of 1/(n^{-10)}	\sum\:_{n=1}^{\infty\:}\frac{1}{n^{-10}}
tangent of y=x^2+x+3	tangent\:y=x^{2}+x+3
tangent of 1/(sqrt(x)),\at x=9	tangent\:\frac{1}{\sqrt{x}},\at\:x=9
derivative of x(x-1)	\frac{d}{dx}(x(x-1))
limit as x approaches 0+of tan^x(5x)	\lim\:_{x\to\:0+}(\tan^{x}(5x))
xy^'+(1-x)y=1	xy^{\prime\:}+(1-x)y=1
integral of e^{(x^2)/2}x	\int\:e^{\frac{x^{2}}{2}}xdx
limit as x approaches infinity of sqrt(x)*e^{-x/2}	\lim\:_{x\to\:\infty\:}(\sqrt{x}\cdot\:e^{-\frac{x}{2}})
area y=4-x^2,y=x^2-4	area\:y=4-x^{2},y=x^{2}-4
derivative of Cxe^{4x}	\frac{d}{dx}(Cxe^{4x})
integral of x/(sqrt(x+11))	\int\:\frac{x}{\sqrt{x+11}}dx
xy^'+y=ex	xy^{\prime\:}+y=ex
sum from n=1 to infinity of (3n)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{3n}{n+1}
integral of ((-2x+4))/((x^2+1)(x-1)^2)	\int\:\frac{(-2x+4)}{(x^{2}+1)(x-1)^{2}}dx
derivative of x^{2sin(x})	\frac{d}{dx}(x^{2\sin(x)})
derivative of f(x)=2pix^2	derivative\:f(x)=2πx^{2}
derivative of f(x)=2x^2ln(2x)	derivative\:f(x)=2x^{2}\ln(2x)
(\partial)/(\partial x)((ln(x^2+y^2))^{1/2})	\frac{\partial\:}{\partial\:x}((\ln(x^{2}+y^{2}))^{\frac{1}{2}})
integral of (x-2y)	\int\:(x-2y)dy
tangent of (18)/x	tangent\:\frac{18}{x}
integral of t^{-4}	\int\:t^{-4}dt
derivative of (x^2+x-2/(x^3+6))	\frac{d}{dx}(\frac{x^{2}+x-2}{x^{3}+6})
solvefor y,ln(xy9)=xy	solvefor\:y,\ln(xy9)=xy
area y= 1/2 x^3+2,y=x+1,x=0,x=2	area\:y=\frac{1}{2}x^{3}+2,y=x+1,x=0,x=2
limit as x approaches infinity of 1+(2^{x+1})/(2^x-1)	\lim\:_{x\to\:\infty\:}(1+\frac{2^{x+1}}{2^{x}-1})
integral of 3/(ysqrt(4-(ln(y))^2))	\int\:\frac{3}{y\sqrt{4-(\ln(y))^{2}}}dy
sum from n=1 to infinity of 1/((n+7)n)	\sum\:_{n=1}^{\infty\:}\frac{1}{(n+7)n}
tangent of f(x)=sqrt(x-2),(6,2)	tangent\:f(x)=\sqrt{x-2},(6,2)
(dy)/(dx)7+e^{-5x}y=0	\frac{dy}{dx}7+e^{-5x}y=0
derivative of f(x)=arctan(x^2)	derivative\:f(x)=\arctan(x^{2})
tangent of (ln(x^2-10x-10)),\at x=11	tangent\:(\ln(x^{2}-10x-10)),\at\:x=11
(x^2+1)((dy)/(dx))+3x(y-1)=0,y(0)=8	(x^{2}+1)(\frac{dy}{dx})+3x(y-1)=0,y(0)=8
limit as x approaches-3 of xsqrt(x+3)	\lim\:_{x\to\:-3}(x\sqrt{x+3})
(\partial)/(\partial z)(6ze^{xyz})	\frac{\partial\:}{\partial\:z}(6ze^{xyz})
integral of (sqrt(5+2tan(x)))/(cos^2(x))	\int\:\frac{\sqrt{5+2\tan(x)}}{\cos^{2}(x)}dx
integral of sqrt(-x^2+4x+5)	\int\:\sqrt{-x^{2}+4x+5}dx
derivative of f(x)=-8sqrt(x)	derivative\:f(x)=-8\sqrt{x}
derivative of (arccos(x)/((x+1)^2))	\frac{d}{dx}(\frac{\arccos(x)}{(x+1)^{2}})
derivative of e^{{g}(x}sin(x))	\frac{d}{dx}(e^{{g}(x)}\sin(x))
integral from-infinity to 12 of xe^{x/4}	\int\:_{-\infty\:}^{12}xe^{\frac{x}{4}}dx
implicit (dy)/(dx),3x^2+2y^2=30	implicit\:\frac{dy}{dx},3x^{2}+2y^{2}=30
(\partial)/(\partial x)(x^3+e^y)	\frac{\partial\:}{\partial\:x}(x^{3}+e^{y})
derivative of ln(x/6)	\frac{d}{dx}(\ln(\frac{x}{6}))
integral of csc(pix)cot(pix)	\int\:\csc(πx)\cot(πx)dx
laplacetransform e^{-t}*cos(2t)	laplacetransform\:e^{-t}\cdot\:\cos(2t)
integral of e^{2x+2}	\int\:e^{2x+2}dx
integral of x^{3/4}+6	\int\:x^{\frac{3}{4}}+6dx
y^{'''}-6y^{''}-7y^'=0	y^{\prime\:\prime\:\prime\:}-6y^{\prime\:\prime\:}-7y^{\prime\:}=0
integral of t^3	\int\:t^{3}dt
integral of (((x^3-3x^2+3))/((x-3)))	\int\:(\frac{(x^{3}-3x^{2}+3)}{(x-3)})dx
limit as x approaches 0 of ((-6+x)^2-36)/x	\lim\:_{x\to\:0}(\frac{(-6+x)^{2}-36}{x})

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