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Popular Calculus Problems

(dy)/(dx)=e^{3x+5y}	\frac{dy}{dx}=e^{3x+5y}
integral of 4tan^3(x)sec^2(x)	\int\:4\tan^{3}(x)\sec^{2}(x)dx
derivative of (x^2+1arctan(x))	\frac{d}{dx}((x^{2}+1)\arctan(x))
integral of 1/(x^2)-4/(x^3)	\int\:\frac{1}{x^{2}}-\frac{4}{x^{3}}dx
limit as x approaches 0-of 1/(x^3)	\lim\:_{x\to\:0-}(\frac{1}{x^{3}})
limit as x approaches 0-of x^x	\lim\:_{x\to\:0-}(x^{x})
integral of (3x^5-2x^3+3)/(x^2)	\int\:\frac{3x^{5}-2x^{3}+3}{x^{2}}dx
derivative of 4^x-7	\frac{d}{dx}(4^{x}-7)
(dy)/(dx)+y/x =3x^9y^2	\frac{dy}{dx}+\frac{y}{x}=3x^{9}y^{2}
integral from-4 to 4 of (1+sqrt(16-x^2))	\int\:_{-4}^{4}(1+\sqrt{16-x^{2}})dx
derivative of (8x/((x^2+4)^2))	\frac{d}{dx}(\frac{8x}{(x^{2}+4)^{2}})
integral of (x^5)/(x^6+7)	\int\:\frac{x^{5}}{x^{6}+7}dx
(\partial)/(\partial x)(4/3 pir^3)	\frac{\partial\:}{\partial\:x}(\frac{4}{3}πr^{3})
tangent of (x^2-3x+3)sqrt(25-x^2)	tangent\:(x^{2}-3x+3)\sqrt{25-x^{2}}
integral of (x^2)/(x+8)	\int\:\frac{x^{2}}{x+8}dx
integral of 1/(x\sqrt[3]{x)}	\int\:\frac{1}{x\sqrt[3]{x}}dx
integral from 1 to 8 of x/(x^2+4x+13)	\int\:_{1}^{8}\frac{x}{x^{2}+4x+13}dx
derivative of f(x)=sqrt(2-2x)	derivative\:f(x)=\sqrt{2-2x}
f^{''}(x)=x^2,f^'(0)=6,f(0)=3	f^{\prime\:\prime\:}(x)=x^{2},f^{\prime\:}(0)=6,f(0)=3
limit as x approaches infinity of (8-e^x)/(8+3e^x)	\lim\:_{x\to\:\infty\:}(\frac{8-e^{x}}{8+3e^{x}})
integral of (ln(3x))/(2x)	\int\:\frac{\ln(3x)}{2x}dx
taylor e^x+e^{-3x}	taylor\:e^{x}+e^{-3x}
integral of 9sin^2(x)	\int\:9\sin^{2}(x)dx
integral from 0 to pi/4 of 10sec^2(x)	\int\:_{0}^{\frac{π}{4}}10\sec^{2}(x)dx
(\partial)/(\partial x)(cos(xe^{xy}))	\frac{\partial\:}{\partial\:x}(\cos(xe^{xy}))
sum from n=1 to infinity of 4/(3n)	\sum\:_{n=1}^{\infty\:}\frac{4}{3n}
limit as x approaches 0 of x^4cos(9/x)	\lim\:_{x\to\:0}(x^{4}\cos(\frac{9}{x}))
laplacetransform t-sin(t)	laplacetransform\:t-\sin(t)
derivative of ln(sqrt(2x+1))	derivative\:\ln(\sqrt{2x+1})
integral from 0 to 3/4 of 30x	\int\:_{0}^{\frac{3}{4}}30xdx
derivative of f(x)=sqrt(x)+\sqrt[9]{x}	derivative\:f(x)=\sqrt{x}+\sqrt[9]{x}
limit as x approaches-infinity of cos(x)	\lim\:_{x\to\:-\infty\:}(\cos(x))
derivative of ln(x+1+x/(x+1))	\frac{d}{dx}(\ln(x+1)+\frac{x}{x+1})
limit as x approaches 2 of x^2+1	\lim\:_{x\to\:2}(x^{2}+1)
derivative of 3+e^{-x}	\frac{d}{dx}(3+e^{-x})
derivative of 1/(x^2-5)	\frac{d}{dx}(\frac{1}{x^{2}-5})
derivative of f(x)=(x^2+3)(x^2-3)x^2	derivative\:f(x)=(x^{2}+3)(x^{2}-3)x^{2}
integral of 1/(cos^2(x)sqrt(1-tan^2(x)))	\int\:\frac{1}{\cos^{2}(x)\sqrt{1-\tan^{2}(x)}}dx
y^{''}-6y^'=36t	y^{\prime\:\prime\:}-6y^{\prime\:}=36t
sum from n=0 to infinity of (n!)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{2^{n}}
limit as x approaches-infinity of x^2ex	\lim\:_{x\to\:-\infty\:}(x^{2}ex)
(\partial)/(\partial y)(4-x^2-2y^2)	\frac{\partial\:}{\partial\:y}(4-x^{2}-2y^{2})
derivative of (x-2ln(x-1)/(x-1))	\frac{d}{dx}(\frac{x-2\ln(x)-1}{x-1})
limit as x approaches 0 of (x+1/x)*e^{-1/(x^2)}	\lim\:_{x\to\:0}((x+\frac{1}{x})\cdot\:e^{-\frac{1}{x^{2}}})
derivative of y=4x^2-3	derivative\:y=4x^{2}-3
limit as x approaches 0 of ((9x^2-2x))/x	\lim\:_{x\to\:0}(\frac{(9x^{2}-2x)}{x})
derivative of (x^2-1/(2x-3))	\frac{d}{dx}(\frac{x^{2}-1}{2x-3})
integral from 0 to 1 of (x-x^k)	\int\:_{0}^{1}(x-x^{k})dx
integral of (x^2+1)/(x^3+3x^2-4)	\int\:\frac{x^{2}+1}{x^{3}+3x^{2}-4}dx
limit as x approaches-2 of x+1	\lim\:_{x\to\:-2}(x+1)
y^'=e^{9x}-8x	y^{\prime\:}=e^{9x}-8x
derivative of (60)/(0.01x^2+1)	derivative\:\frac{60}{0.01x^{2}+1}
(\partial)/(\partial x)(y^{1/2}+x^{1/2})	\frac{\partial\:}{\partial\:x}(y^{\frac{1}{2}}+x^{\frac{1}{2}})
tangent of f(x)=8x^2+5x,\at 53	tangent\:f(x)=8x^{2}+5x,\at\:53
laplacetransform e^{20t+20}	laplacetransform\:e^{20t+20}
(\partial)/(\partial y)(\|x\|y+2x)	\frac{\partial\:}{\partial\:y}(\left\|x\right\|y+2x)
derivative of sqrt(3(1-x^2))	\frac{d}{dx}(\sqrt{3(1-x^{2})})
derivative of-8sin(x)	\frac{d}{dx}(-8\sin(x))
limit as x approaches 2 of sqrt(((2x^2+1))/((3x-2)))	\lim\:_{x\to\:2}(\sqrt{\frac{(2x^{2}+1)}{(3x-2)}})
sum from n=2 to infinity of 1/(n^{1.5)}	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{1.5}}
derivative of y=16^{sin(x^2)}	derivative\:y=16^{\sin(x^{2})}
slope of (2.3)(-2.3)	slope\:(2.3)(-2.3)
(\partial)/(\partial x)(-x^{-2})	\frac{\partial\:}{\partial\:x}(-x^{-2})
integral of (x^5-9x^3-9x^2-9)/(x^3+9x)	\int\:\frac{x^{5}-9x^{3}-9x^{2}-9}{x^{3}+9x}dx
derivative of (e^x/(sqrt(e^x+1)))	\frac{d}{dx}(\frac{e^{x}}{\sqrt{e^{x}+1}})
integral from 1 to 4 of (x^2+3)/(5x-x^2)	\int\:_{1}^{4}\frac{x^{2}+3}{5x-x^{2}}dx
sum from n=1 to infinity of \sqrt[n]{n}	\sum\:_{n=1}^{\infty\:}\sqrt[n]{n}
derivative of f(x)=tan((3pi)/4 x)	derivative\:f(x)=\tan(\frac{3π}{4}x)
integral of a^{-x}	\int\:a^{-x}dx
limit as x approaches 3-of arcsin(x/3)	\lim\:_{x\to\:3-}(\arcsin(\frac{x}{3}))
simplify 1/(sqrt(3x))	simplify\:\frac{1}{\sqrt{3x}}
integral of 15sin^2(x)	\int\:15\sin^{2}(x)dx
derivative of (x+ln(x)^5)	\frac{d}{dx}((x+\ln(x))^{5})
integral from 0 to 3 of 2x^2	\int\:_{0}^{3}2x^{2}dx
limit as x approaches infinity of pi^{2x}	\lim\:_{x\to\:\infty\:}(π^{2x})
y^'=x^2-2,y(3)=7	y^{\prime\:}=x^{2}-2,y(3)=7
(\partial)/(\partial x)(xy+yz-xz)	\frac{\partial\:}{\partial\:x}(xy+yz-xz)
inverse oflaplace 1/((s^2+1)(s^2+2s+3))	inverselaplace\:\frac{1}{(s^{2}+1)(s^{2}+2s+3)}
integral of (cos(x))/(cos^3(x))	\int\:\frac{\cos(x)}{\cos^{3}(x)}dx
derivative of (cos(x))^x	derivative\:(\cos(x))^{x}
limit as x approaches 2 of log_{10}(x-2)	\lim\:_{x\to\:2}(\log_{10}(x-2))
limit as x approaches 0 of (1-2x)^{1/(x^2)}	\lim\:_{x\to\:0}((1-2x)^{\frac{1}{x^{2}}})
f(x)=sin^2(sqrt(x))	f(x)=\sin^{2}(\sqrt{x})
integral from 0 to pi/2 of-7cos^5(x)	\int\:_{0}^{\frac{π}{2}}-7\cos^{5}(x)dx
y^{''}+4y^'+11y=0	y^{\prime\:\prime\:}+4y^{\prime\:}+11y=0
derivative of ((0.9-0.4x)/x)	\frac{d}{dx}(\frac{(0.9-0.4x)}{x})
laplacetransform 2sin(5t)	laplacetransform\:2\sin(5t)
integral of xcos(kx)	\int\:x\cos(kx)dx
y^{''}+0.1y^'+0.0004y=1	y^{\prime\:\prime\:}+0.1y^{\prime\:}+0.0004y=1
sum from n=1 to infinity of (2/3)^{2n}	\sum\:_{n=1}^{\infty\:}(\frac{2}{3})^{2n}
integral from 0 to ln(13) of xe^x	\int\:_{0}^{\ln(13)}xe^{x}dx
integral of 1/(sqrt(6r-7))	\int\:\frac{1}{\sqrt{6r-7}}dr
integral of sec^2(x)csc^4(x)	\int\:\sec^{2}(x)\csc^{4}(x)dx
derivative of y=sqrt(2x-1/2)	derivative\:y=\sqrt{2x-\frac{1}{2}}
integral of 5x^{-2}	\int\:5x^{-2}dx
integral of 5x^6	\int\:5x^{6}dx
derivative of arctan((sqrt(1+x^2)-1/x))	\frac{d}{dx}(\arctan(\frac{\sqrt{1+x^{2}}-1}{x}))
integral of x^2(5x^3-4)^4	\int\:x^{2}(5x^{3}-4)^{4}dx
(dy)/(dx)=y^2-(xy)^2	\frac{dy}{dx}=y^{2}-(xy)^{2}
derivative of-2x^5+6x^4-4x^3-4x^2+6x-2	\frac{d}{dx}(-2x^{5}+6x^{4}-4x^{3}-4x^{2}+6x-2)

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