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Popular Calculus Problems

integral of 3/(xsqrt(x^2-1))	\int\:\frac{3}{x\sqrt{x^{2}-1}}dx
derivative of f(x)=4x-9x^2	\frac{d}{dx}f(x)=4x-9x^{2}
integral from 2 to 4 of x(((2x-3))/6)	\int\:_{2}^{4}x(\frac{(2x-3)}{6})dx
integral of (5x+14)/((x+1)(x^2-4))	\int\:\frac{5x+14}{(x+1)(x^{2}-4)}dx
limit as x approaches pi/2 of e^{sec(x)}	\lim\:_{x\to\:\frac{π}{2}}(e^{\sec(x)})
inverse oflaplace 3/((s+2)^2)	inverselaplace\:\frac{3}{(s+2)^{2}}
integral of (x^2+x)/(x^3-x^2-2x)	\int\:\frac{x^{2}+x}{x^{3}-x^{2}-2x}dx
integral of 5(3x-1)7	\int\:5(3x-1)7dx
taylor ln(3-x)	taylor\:\ln(3-x)
integral of 1/(1+28x)	\int\:\frac{1}{1+28x}dx
derivative of tan(x*107.55)	\frac{d}{dx}(\tan(x)\cdot\:107.55)
derivative of (x^{10}/(20)+1/(16x^8))	\frac{d}{dx}(\frac{x^{10}}{20}+\frac{1}{16x^{8}})
integral of \sqrt[3]{x}+10\sqrt[5]{x}	\int\:\sqrt[3]{x}+10\sqrt[5]{x}dx
(\partial)/(\partial x)(e^{y/x})	\frac{\partial\:}{\partial\:x}(e^{\frac{y}{x}})
integral of x^2+3	\int\:x^{2}+3dx
integral from 0 to 1 of 2/3 x^2(x+1)	\int\:_{0}^{1}\frac{2}{3}x^{2}(x+1)dx
derivative of (tan(x)-20)/(sec(x))	derivative\:\frac{\tan(x)-20}{\sec(x)}
integral of 4(tan^2(x)+tan^4(x))	\int\:4(\tan^{2}(x)+\tan^{4}(x))dx
y^{''}-6y^'+5y=0	y^{\prime\:\prime\:}-6y^{\prime\:}+5y=0
(\partial)/(\partial x)(5-x^2+xy-3y^2)	\frac{\partial\:}{\partial\:x}(5-x^{2}+xy-3y^{2})
derivative of h(x)=ln(x+sqrt(x^2-11))	derivative\:h(x)=\ln(x+\sqrt{x^{2}-11})
area sqrt(x), 1/2 x	area\:\sqrt{x},\frac{1}{2}x
x^2y^{''}-2xy^'+2y=x^4e^x	x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=x^{4}e^{x}
integral of 1/2 y^2	\int\:\frac{1}{2}y^{2}dy
inverse oflaplace (s+2)/(s^2+4s+5)	inverselaplace\:\frac{s+2}{s^{2}+4s+5}
y^{''}+25y=tsin(4t)	y^{\prime\:\prime\:}+25y=t\sin(4t)
(\partial)/(\partial w)(w/u)	\frac{\partial\:}{\partial\:w}(\frac{w}{u})
limit as x approaches 0 of (e^x-x-1)/x	\lim\:_{x\to\:0}(\frac{e^{x}-x-1}{x})
derivative of 8^x	derivative\:8^{x}
derivative of (cot(x)/(1-sin(x)))	\frac{d}{dx}(\frac{\cot(x)}{1-\sin(x)})
derivative of sin(8xe^{4x})	\frac{d}{dx}(\sin(8x)e^{4x})
derivative of ln(x^2-4)	derivative\:\ln(x^{2}-4)
integral of sin(x)(-8xcos(2x))	\int\:\sin(x)(-8x\cos(2x))dx
limit as x approaches 0 of 3x+2	\lim\:_{x\to\:0}(3x+2)
f(x)= 2/(3x)	f(x)=\frac{2}{3x}
derivative of 2xe^{-2sqrt(x)}	derivative\:2xe^{-2\sqrt{x}}
integral of 1/((x^2-4)^{3/2)}	\int\:\frac{1}{(x^{2}-4)^{\frac{3}{2}}}dx
integral of sin(8x+2)	\int\:\sin(8x+2)dx
2*y^{''}+y^'-y=0	2\cdot\:y^{\prime\:\prime\:}+y^{\prime\:}-y=0
y^{''}+2y^'=2t+5-e^{-2t}	y^{\prime\:\prime\:}+2y^{\prime\:}=2t+5-e^{-2t}
derivative of x^{2-2x}	\frac{d}{dx}(x^{2-2x})
derivative of y=(ln(x))/(e^x)	derivative\:y=\frac{\ln(x)}{e^{x}}
integral of csc(6x)	\int\:\csc(6x)dx
inverse oflaplace (2s)/(s^2+2s+1)	inverselaplace\:\frac{2s}{s^{2}+2s+1}
integral from 0 to pi/4 of (sin(x))	\int\:_{0}^{\frac{π}{4}}(\sin(x))dx
derivative of (sqrt(x)/(sqrt(x+1)))	\frac{d}{dx}(\frac{\sqrt{x}}{\sqrt{x+1}})
tangent of f(x)=8x(x+2),\at x=3	tangent\:f(x)=8x(x+2),\at\:x=3
derivative of t^3-1/(\sqrt[4]{t^5)}	derivative\:t^{3}-\frac{1}{\sqrt[4]{t^{5}}}
integral of cot^3(x)csc^5(x)	\int\:\cot^{3}(x)\csc^{5}(x)dx
integral of sin(2x)cos^5(2x)	\int\:\sin(2x)\cos^{5}(2x)dx
(\partial)/(\partial x)(x^4sin(y^9z^9))	\frac{\partial\:}{\partial\:x}(x^{4}\sin(y^{9}z^{9}))
integral of \sqrt[3]{x+4}	\int\:\sqrt[3]{x+4}dx
limit as x approaches 5 of (x^2-25)/(3x-15)	\lim\:_{x\to\:5}(\frac{x^{2}-25}{3x-15})
derivative of sqrt((1-x)^2+x^3)	derivative\:\sqrt{(1-x)^{2}+x^{3}}
limit as x approaches 5 of 1/(x^2+x)	\lim\:_{x\to\:5}(\frac{1}{x^{2}+x})
integral of 1/(sqrt(-2x^2+8x+4))	\int\:\frac{1}{\sqrt{-2x^{2}+8x+4}}dx
integral from 0 to 3 of (2x-x^2)^3(1-x)	\int\:_{0}^{3}(2x-x^{2})^{3}(1-x)dx
(\partial)/(\partial x)(z^2cos(yx))	\frac{\partial\:}{\partial\:x}(z^{2}\cos(yx))
y^'-6/x y=((y^3))/(x^4)	y^{\prime\:}-\frac{6}{x}y=\frac{(y^{3})}{x^{4}}
integral from 4 to 9 of xsqrt(x)	\int\:_{4}^{9}x\sqrt{x}dx
integral of 1/(x^2sqrt(x^2-196))	\int\:\frac{1}{x^{2}\sqrt{x^{2}-196}}dx
integral of (e^x(2x^3+x^2-4x-6))/(6x^4)	\int\:\frac{e^{x}(2x^{3}+x^{2}-4x-6)}{6x^{4}}dx
limit as t approaches 0 of (sin(2t))/t	\lim\:_{t\to\:0}(\frac{\sin(2t)}{t})
limit as x approaches 0+of sin(x)*ln(x)	\lim\:_{x\to\:0+}(\sin(x)\cdot\:\ln(x))
4y^{''}-9y=0	4y^{\prime\:\prime\:}-9y=0
derivative of y= 1/(t+1)	derivative\:y=\frac{1}{t+1}
derivative of 1/4 x^3-2x	\frac{d}{dx}(\frac{1}{4}x^{3}-2x)
derivative of sin(e^{-x})	\frac{d}{dx}(\sin(e^{-x}))
limit as x approaches infinity of 1/x+6	\lim\:_{x\to\:\infty\:}(\frac{1}{x}+6)
y^'=-3(1-y)(1-2y)	y^{\prime\:}=-3(1-y)(1-2y)
integral from 0 to 24 of x/(sqrt(9+3x))	\int\:_{0}^{24}\frac{x}{\sqrt{9+3x}}dx
limit as x approaches 0 of (sin(1))/x	\lim\:_{x\to\:0}(\frac{\sin(1)}{x})
taylor ln(x+3),-1	taylor\:\ln(x+3),-1
d/(dt)((t^4-2t)^2-5)	\frac{d}{dt}((t^{4}-2t)^{2}-5)
integral from 0 to 9 of 81-x^2	\int\:_{0}^{9}81-x^{2}dx
implicit x^y=y^x	implicit\:x^{y}=y^{x}
integral of (x^3)/(e^{x^4)}	\int\:\frac{x^{3}}{e^{x^{4}}}dx
(\partial)/(\partial z)(3y)	\frac{\partial\:}{\partial\:z}(3y)
derivative of ln(sqrt(1-2x))	derivative\:\ln(\sqrt{1-2x})
integral from 0 to-pi/2 of sin^5(x)	\int\:_{0}^{-\frac{π}{2}}\sin^{5}(x)dx
integral of (10x)^n	\int\:(10x)^{n}dx
integral from 2 to 5 of 2x^3	\int\:_{2}^{5}2x^{3}dx
(dy)/(dx)=-y^3	\frac{dy}{dx}=-y^{3}
tangent of y=x^2-8x+9,(1,2)	tangent\:y=x^{2}-8x+9,(1,2)
derivative of ue^{-x}	\frac{d}{dx}(ue^{-x})
integral of sqrt(361-x^2)	\int\:\sqrt{361-x^{2}}dx
integral of-2x^{-1}	\int\:-2x^{-1}dx
integral of ((e^x)/3+2x)	\int\:(\frac{e^{x}}{3}+2x)dx
integral of tan^5(x)*sec^3(x)	\int\:\tan^{5}(x)\cdot\:\sec^{3}(x)dx
(dy)/(dx)=-4^{-2}-y^{-1}+y^{-1}+y	\frac{dy}{dx}=-4^{-2}-y^{-1}+y^{-1}+y
y^{''}-3/x y^'-(12)/(x^2)y=4x^2	y^{\prime\:\prime\:}-\frac{3}{x}y^{\prime\:}-\frac{12}{x^{2}}y=4x^{2}
integral of 1/(xsqrt(36x^2-1))	\int\:\frac{1}{x\sqrt{36x^{2}-1}}dx
integral of 6x^2e^{6x}	\int\:6x^{2}e^{6x}dx
area y=x^3+x^2-6x,y=6x	area\:y=x^{3}+x^{2}-6x,y=6x
laplacetransform e^{(3t)}(4cos(3t)-10/3 sin(3t))	laplacetransform\:e^{(3t)}(4\cos(3t)-\frac{10}{3}\sin(3t))
limit as x approaches-1+of x/(\|x+1\|)	\lim\:_{x\to\:-1+}(\frac{x}{\left\|x+1\right\|})
solvefor y,y=xe^y	solvefor\:y,y=xe^{y}
integral from-3 to-2 of (2x(3-x^2)^3)	\int\:_{-3}^{-2}(2x(3-x^{2})^{3})dx
tangent of f(x)=cos(x),\at x=pi	tangent\:f(x)=\cos(x),\at\:x=π
inverse oflaplace (e^{-4s})/(s(s^2+16))	inverselaplace\:\frac{e^{-4s}}{s(s^{2}+16)}

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