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Popular Calculus Problems

limit as t approaches infinity of 1/(5t)	\lim\:_{t\to\:\infty\:}(\frac{1}{5t})
integral of \sqrt[7]{tan(8x)}sec^2(8x)	\int\:\sqrt[7]{\tan(8x)}\sec^{2}(8x)dx
integral from 0 to 1 of 1/(x^2-4)	\int\:_{0}^{1}\frac{1}{x^{2}-4}dx
d/(dy)(sqrt((y-4)^3))	\frac{d}{dy}(\sqrt{(y-4)^{3}})
integral of ln(y^2+2)	\int\:\ln(y^{2}+2)dy
integral of 81x^2-18+1/(x^2)	\int\:81x^{2}-18+\frac{1}{x^{2}}dx
integral of (-5x^3-1/x+5/(x^4)+6sqrt(x))	\int\:(-5x^{3}-\frac{1}{x}+\frac{5}{x^{4}}+6\sqrt{x})dx
integral of x+6	\int\:x+6dx
integral of tln(t)	\int\:t\ln(t)dt
(\partial)/(\partial x)(ln(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\ln(x^{2}-y^{2}))
integral from 1 to 2 of (2x+1)/(x^2+x)	\int\:_{1}^{2}\frac{2x+1}{x^{2}+x}dx
integral from 1 to 3 of 4x^3-8x+1	\int\:_{1}^{3}4x^{3}-8x+1dx
derivative of 9tsin(pit)	derivative\:9t\sin(πt)
maclaurin 1/((1-x)^3)	maclaurin\:\frac{1}{(1-x)^{3}}
integral of-2x^2+4	\int\:-2x^{2}+4dx
integral of (-e^{2-x})	\int\:(-e^{2-x})dx
ydx+x(ln(x)-ln(y)-1)dy=0	ydx+x(\ln(x)-\ln(y)-1)dy=0
integral of 1/(x^2+2x+50)	\int\:\frac{1}{x^{2}+2x+50}dx
inverse oflaplace ((s+2))/((s-1)(s+6))	inverselaplace\:\frac{(s+2)}{(s-1)(s+6)}
limit as x approaches pi/2 of cos(x)	\lim\:_{x\to\:\frac{π}{2}}(\cos(x))
integral of 1/(xsqrt(x^2-64))	\int\:\frac{1}{x\sqrt{x^{2}-64}}dx
integral of x\sqrt[3]{x-4}	\int\:x\sqrt[3]{x-4}dx
integral of (x^2)/(12)	\int\:\frac{x^{2}}{12}dx
derivative of f(x)=8sqrt(6x^2+7)	derivative\:f(x)=8\sqrt{6x^{2}+7}
integral of ((x+2)/(sqrt(x^2+4x)))	\int\:(\frac{x+2}{\sqrt{x^{2}+4x}})dx
derivative of (6x^2+8x+2/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+8x+2}{\sqrt{x}})
integral of (7x)/((x^2+2)^2)	\int\:\frac{7x}{(x^{2}+2)^{2}}dx
(\partial)/(\partial y)(xycos(z))	\frac{\partial\:}{\partial\:y}(xy\cos(z))
integral of sin(xy)	\int\:\sin(xy)dx
integral from-1 to x of 1.5x^2	\int\:_{-1}^{x}1.5x^{2}dx
derivative of f(x)=(x^5+4x)/(x^3)	derivative\:f(x)=\frac{x^{5}+4x}{x^{3}}
y^'=(1-y)*sin(x)	y^{\prime\:}=(1-y)\cdot\:\sin(x)
integral from 2 to 3 of (18)/(sqrt(3-x))	\int\:_{2}^{3}\frac{18}{\sqrt{3-x}}dx
integral of (3x^2+2)/((x^2-2x+2)^2)	\int\:\frac{3x^{2}+2}{(x^{2}-2x+2)^{2}}dx
y^{''''}+2y^{''}+y=0	y^{\prime\:\prime\:\prime\:\prime\:}+2y^{\prime\:\prime\:}+y=0
derivative of e^{7x}	derivative\:e^{7x}
derivative of f(x)=sqrt(3x+2)	derivative\:f(x)=\sqrt{3x+2}
derivative of 20(e^{-x}-e^{-2x})	\frac{d}{dx}(20(e^{-x}-e^{-2x}))
laplacetransform 21e^t	laplacetransform\:21e^{t}
integral from 0 to 4 of 2pi(y)(3y+4-y^2)	\int\:_{0}^{4}2π(y)(3y+4-y^{2})dy
integral from 0 to 1/2 of xcos(pi)x	\int\:_{0}^{\frac{1}{2}}x\cos(π)xdx
integral from 0 to 1.75 of 600x	\int\:_{0}^{1.75}600xdx
limit as x approaches 0 of e^{8/x}	\lim\:_{x\to\:0}(e^{\frac{8}{x}})
derivative of f(y)= A/(y^9)+Be^y	derivative\:f(y)=\frac{A}{y^{9}}+Be^{y}
limit as x approaches 2-of 3/(x-2)	\lim\:_{x\to\:2-}(\frac{3}{x-2})
derivative of (cos(x)^2+sin(x^2))	\frac{d}{dx}((\cos(x))^{2}+\sin(x^{2}))
integral of x/((x^2+R^2)^{3/2)}	\int\:\frac{x}{(x^{2}+R^{2})^{\frac{3}{2}}}dx
integral of (x^2+3x)2^x	\int\:(x^{2}+3x)2^{x}dx
integral of (x^3+4x-13)/(x^2+4)	\int\:\frac{x^{3}+4x-13}{x^{2}+4}dx
derivative of 2sin^5(sqrt(x))	derivative\:2\sin^{5}(\sqrt{x})
integral of 13	\int\:13dx
limit as x approaches 7 of 5x^{-1}	\lim\:_{x\to\:7}(5x^{-1})
integral of x/(x^2-2x-3)	\int\:\frac{x}{x^{2}-2x-3}dx
limit as x approaches 1 of (x^4-1)/(x^3-1)	\lim\:_{x\to\:1}(\frac{x^{4}-1}{x^{3}-1})
tangent of 3x-32sqrt(x),\at x=4	tangent\:3x-32\sqrt{x},\at\:x=4
area y=x^2-12,y=x-6	area\:y=x^{2}-12,y=x-6
(\partial)/(\partial x)(x+(x-y)/(y-z))	\frac{\partial\:}{\partial\:x}(x+\frac{x-y}{y-z})
derivative of tan(cos(x/2))	\frac{d}{dx}(\tan(\cos(\frac{x}{2})))
integral of e^{x^3+5}*x^2	\int\:e^{x^{3}+5}\cdot\:x^{2}dx
integral of (8-e^x)/(e^{5x)}	\int\:\frac{8-e^{x}}{e^{5x}}dx
limit as x approaches 2 of sqrt(x-1)-2x	\lim\:_{x\to\:2}(\sqrt{x-1}-2x)
derivative of 3^xtan(ln(x))	derivative\:3^{x}\tan(\ln(x))
integral of x/(x^4)	\int\:\frac{x}{x^{4}}dx
integral of sqrt(sin(x))*cos(x)	\int\:\sqrt{\sin(x)}\cdot\:\cos(x)dx
slope of y=3+4x^2-2x^3	slope\:y=3+4x^{2}-2x^{3}
integral of (-cos(x))	\int\:(-\cos(x))dx
tangent of f(x)= 1/(2sqrt(x+1))	tangent\:f(x)=\frac{1}{2\sqrt{x+1}}
d/(dt)(5cos(2t))	\frac{d}{dt}(5\cos(2t))
limit as x approaches 0 of (tan(x))/(3x)	\lim\:_{x\to\:0}(\frac{\tan(x)}{3x})
tangent of f(x)=-3x^2-5x+1	tangent\:f(x)=-3x^{2}-5x+1
integral of cos^4(t)	\int\:\cos^{4}(t)dt
ydy=4x(y^2+1)^{1/2}dx	ydy=4x(y^{2}+1)^{\frac{1}{2}}dx
integral of (7x^3+4x)/(x-1)	\int\:\frac{7x^{3}+4x}{x-1}dx
y^{''}+25y=-40sin(5t)	y^{\prime\:\prime\:}+25y=-40\sin(5t)
x^2y^'-2xy=y^4	x^{2}y^{\prime\:}-2xy=y^{4}
derivative of cos^2(sqrt(tan(\sqrt{x)}))	\frac{d}{dx}(\cos^{2}(\sqrt{\tan(\sqrt{x})}))
limit as x approaches 0 of (5x)/(x^3)	\lim\:_{x\to\:0}(\frac{5x}{x^{3}})
derivative of (x-1/(x^2+2x+6))	\frac{d}{dx}(\frac{x-1}{x^{2}+2x+6})
y^'-2y=-5x^2	y^{\prime\:}-2y=-5x^{2}
tangent of f(x)=3e^{-4x},\at x=0	tangent\:f(x)=3e^{-4x},\at\:x=0
inverse oflaplace s/(s^2-2s+10)	inverselaplace\:\frac{s}{s^{2}-2s+10}
derivative of (6x^2+4x+2/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+4x+2}{\sqrt{x}})
d/(dy)((y^4+48)/(24y))	\frac{d}{dy}(\frac{y^{4}+48}{24y})
integral of (x^3-1)/(x^4-4x)	\int\:\frac{x^{3}-1}{x^{4}-4x}dx
(\partial)/(\partial x)(1/(1/x+1/y))	\frac{\partial\:}{\partial\:x}(\frac{1}{\frac{1}{x}+\frac{1}{y}})
(\partial)/(\partial x)(4arctan(xy))	\frac{\partial\:}{\partial\:x}(4\arctan(xy))
integral of 12	\int\:12dx
limit as x approaches 0 of x/(tan(2x))	\lim\:_{x\to\:0}(\frac{x}{\tan(2x)})
sum from n=8 to infinity of (n+3)/(n!)	\sum\:_{n=8}^{\infty\:}\frac{n+3}{n!}
derivative of xsqrt(16-x^2)	derivative\:x\sqrt{16-x^{2}}
integral of (xsqrt(4x^2+7))	\int\:(x\sqrt{4x^{2}+7})dx
integral of (sin^2(θ))	\int\:(\sin^{2}(θ))dθ
integral of e^x-cos(x)	\int\:e^{x}-\cos(x)dx
area x^2+1,1,3	area\:x^{2}+1,1,3
y^'=2x	y^{\prime\:}=2x
y^{''}-3y^'=26sin(2t)	y^{\prime\:\prime\:}-3y^{\prime\:}=26\sin(2t)
integral of (3x^2)/((169+x^2)^2)	\int\:\frac{3x^{2}}{(169+x^{2})^{2}}dx
sum from n=1 to infinity of 4/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{4}{n+1}
sum from n=0 to infinity of n(4/5)^n	\sum\:_{n=0}^{\infty\:}n(\frac{4}{5})^{n}
(\partial)/(\partial x)(cos(2x+2y))	\frac{\partial\:}{\partial\:x}(\cos(2x+2y))

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