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Popular Calculus Problems

y^'+y=5cos(2t)	y^{\prime\:}+y=5\cos(2t)
inverse oflaplace ((3s+7))/(s^2+4s+3)	inverselaplace\:\frac{(3s+7)}{s^{2}+4s+3}
derivative of x^4sin(xsin(3x))	\frac{d}{dx}(x^{4}\cdot\:\sin(x)\cdot\:\sin(3x))
(\partial)/(\partial t)(sqrt(s^2+t^2))	\frac{\partial\:}{\partial\:t}(\sqrt{s^{2}+t^{2}})
integral of (10)/((20x+1)^{23)}	\int\:\frac{10}{(20x+1)^{23}}dx
integral of sec(t)(3sec(t)+5tan(t))	\int\:\sec(t)(3\sec(t)+5\tan(t))dt
derivative of sqrt(((x^2)2^x)^3)	derivative\:\sqrt{((x^{2})2^{x})^{3}}
derivative of 150-1/40 (x-50^2)	\frac{d}{dx}(150-\frac{1}{40}(x-50)^{2})
integral of sin(2u)	\int\:\sin(2u)du
integral of-4/y	\int\:-\frac{4}{y}dy
limit as x approaches pi+of cot(x)	\lim\:_{x\to\:π+}(\cot(x))
(dy)/(dx)=2cos(5x)	\frac{dy}{dx}=2\cos(5x)
parity y=ln(axsqrt(a+x))	parity\:y=\ln(ax\sqrt{a+x})
derivative of arccos(-2x)	\frac{d}{dx}(\arccos(-2x))
derivative of (x^2+4x^{1/2}/(x^2))	\frac{d}{dx}(\frac{x^{2}+4x^{\frac{1}{2}}}{x^{2}})
laplacetransform sin(2pit)	laplacetransform\:\sin(2πt)
area x=5y^2,x=54-y^2	area\:x=5y^{2},x=54-y^{2}
taylor ln(x+2)-1	taylor\:\ln(x+2)-1
integral of (4x^2-16x+7)^4(x-2)	\int\:(4x^{2}-16x+7)^{4}(x-2)dx
integral of 1/(81+x^2)	\int\:\frac{1}{81+x^{2}}dx
limit as x approaches 0 of 0.1ln(0.1)	\lim\:_{x\to\:0}(0.1\ln(0.1))
integral of sin^2(x)(cos(x))	\int\:\sin^{2}(x)(\cos(x))dx
(\partial)/(\partial x)(sqrt(x)*ln(t))	\frac{\partial\:}{\partial\:x}(\sqrt{x}\cdot\:\ln(t))
(dv)/(dt)=9.81-(0.5)/(v^{-1)}	\frac{dv}{dt}=9.81-\frac{0.5}{v^{-1}}
sum from k=0 to infinity of 5*3^k	\sum\:_{k=0}^{\infty\:}5\cdot\:3^{k}
derivative of-(4x)/((x^2-1)^2)	derivative\:-\frac{4x}{(x^{2}-1)^{2}}
limit as x approaches 0+of \|x^2-2x-3\|	\lim\:_{x\to\:0+}(\left\|x^{2}-2x-3\right\|)
(\partial)/(\partial x)(2+yln(4+xy^2))	\frac{\partial\:}{\partial\:x}(2+y\ln(4+xy^{2}))
derivative of x(x^2+4)	derivative\:x(x^{2}+4)
derivative of ((x^2-1))/(x^2+1)	derivative\:\frac{(x^{2}-1)}{x^{2}+1}
integral from-infinity to 0 of z/(z^4+4)	\int\:_{-\infty\:}^{0}\frac{z}{z^{4}+4}dz
5y^{''}+4y^'=0	5y^{\prime\:\prime\:}+4y^{\prime\:}=0
limit as x approaches infinity+of sec(x)	\lim\:_{x\to\:\infty\:+}(\sec(x))
integral of ((x+6))/(sqrt(5-4x-x^2))	\int\:\frac{(x+6)}{\sqrt{5-4x-x^{2}}}dx
y^{''}+y^'=0,y(0)=2,y^'(0)=1	y^{\prime\:\prime\:}+y^{\prime\:}=0,y(0)=2,y^{\prime\:}(0)=1
tangent of f(x)=x^3-3x+4,(3,22)	tangent\:f(x)=x^{3}-3x+4,(3,22)
(\partial)/(\partial x)(-2xz)	\frac{\partial\:}{\partial\:x}(-2xz)
integral of 7x^{11}e^{-x^6}	\int\:7x^{11}e^{-x^{6}}dx
derivative of 4sqrt(2x^2+9)	derivative\:4\sqrt{2x^{2}+9}
derivative of f(x)=-3x^5cos(x)	derivative\:f(x)=-3x^{5}\cos(x)
integral of (x^3)/((1+x^4)^{1/2)}	\int\:\frac{x^{3}}{(1+x^{4})^{\frac{1}{2}}}dx
derivative of f(x)=x^{5/2}e^x	derivative\:f(x)=x^{\frac{5}{2}}e^{x}
integral of sec^2(x)csc(x)	\int\:\sec^{2}(x)\csc(x)dx
integral of 3sin^2(x)cos(x)	\int\:3\sin^{2}(x)\cos(x)dx
inverse oflaplace 6/((s-2)^4*(s+2)^2)	inverselaplace\:\frac{6}{(s-2)^{4}\cdot\:(s+2)^{2}}
integral of x^7-3x+2	\int\:x^{7}-3x+2dx
f(x)=cos(sin(x))	f(x)=\cos(\sin(x))
integral from 0 to 1 of (3x)/(e^{2x)}	\int\:_{0}^{1}\frac{3x}{e^{2x}}dx
area y=\sqrt[4]{x},y=x^2	area\:y=\sqrt[4]{x},y=x^{2}
area x^3,0,2	area\:x^{3},0,2
(\partial)/(\partial s)(-s^2t^2)	\frac{\partial\:}{\partial\:s}(-s^{2}t^{2})
d/(dt)(scos(t))	\frac{d}{dt}(s\cos(t))
implicit (dy)/(dx),x^y=y^x	implicit\:\frac{dy}{dx},x^{y}=y^{x}
limit as x approaches 2 of (x-2)^2	\lim\:_{x\to\:2}((x-2)^{2})
integral of (2x^2-x-20)/(x^2+x-6)	\int\:\frac{2x^{2}-x-20}{x^{2}+x-6}dx
integral of 8xsec(x)tan(x)	\int\:8x\sec(x)\tan(x)dx
(\partial)/(\partial x)(xy(-3-x-y))	\frac{\partial\:}{\partial\:x}(xy(-3-x-y))
integral of 3sec(2)(x)+2x-8x	\int\:3\sec(2)(x)+2x-8xdx
(\partial)/(\partial x)(ln(7x^2+xy))	\frac{\partial\:}{\partial\:x}(\ln(7x^{2}+xy))
y^{''}+3y^'+2y=cos(ex)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=\cos(ex)
integral of (9x^2)/2-5cos(x)+7	\int\:\frac{9x^{2}}{2}-5\cos(x)+7dx
inverse oflaplace-1/(s^2)	inverselaplace\:-\frac{1}{s^{2}}
(\partial)/(\partial x)(y+1/(x+y))	\frac{\partial\:}{\partial\:x}(y+\frac{1}{x+y})
derivative of log_{3}(sec(2x))	\frac{d}{dx}(\log_{3}(\sec(2x)))
limit as x approaches 0 of tan(x)-sec(x)	\lim\:_{x\to\:0}(\tan(x)-\sec(x))
laplacetransform (te)^3e^{-2t}e^{-2}	laplacetransform\:(te)^{3}e^{-2t}e^{-2}
integral of 5x^2\sqrt[3]{x}	\int\:5x^{2}\sqrt[3]{x}dx
integral of sqrt(x)ln^2(x)	\int\:\sqrt{x}\ln^{2}(x)dx
area y=3(x+1),y=4(x+1),x=7	area\:y=3(x+1),y=4(x+1),x=7
derivative of arcsec(x^3)	\frac{d}{dx}(\arcsec(x^{3}))
integral from 0 to 1 of 7cos(2x)	\int\:_{0}^{1}7\cos(2x)dx
integral of x/(x^2+5x+6)	\int\:\frac{x}{x^{2}+5x+6}dx
derivative of 3x^2-18x-21	\frac{d}{dx}(3x^{2}-18x-21)
integral of e^{-t^2}t	\int\:e^{-t^{2}}tdt
sum from n=1 to infinity of 7(0.9)^{n-1}	\sum\:_{n=1}^{\infty\:}7(0.9)^{n-1}
derivative of f(x)=(3x^2+1)^3	derivative\:f(x)=(3x^{2}+1)^{3}
derivative of x/z	\frac{d}{dx}(\frac{x}{z})
integral from 0 to 2pi of sin^2(11x)	\int\:_{0}^{2π}\sin^{2}(11x)dx
taylor 4cos(2x)	taylor\:4\cos(2x)
integral of 1-3/x	\int\:1-\frac{3}{x}dx
integral of xcos(21x)	\int\:x\cos(21x)dx
integral of x^2e^{-x^3}sin^2(x^3)	\int\:x^{2}e^{-x^{3}}\sin^{2}(x^{3})dx
(\partial)/(\partial x)(sin(y-5x))	\frac{\partial\:}{\partial\:x}(\sin(y-5x))
integral of (4x)/(\sqrt[3]{5+3x^2)}	\int\:\frac{4x}{\sqrt[3]{5+3x^{2}}}dx
x^{''}+2x^'+2x=0,x(0)=0,x^'(0)=1	x^{\prime\:\prime\:}+2x^{\prime\:}+2x=0,x(0)=0,x^{\prime\:}(0)=1
integral of (x^3-27)/(x-3)	\int\:\frac{x^{3}-27}{x-3}dx
integral from 2 to 5 of 6sqrt(x)	\int\:_{2}^{5}6\sqrt{x}dx
y^'+2y=e^{-2t}	y^{\prime\:}+2y=e^{-2t}
limit as x approaches 0 of (e^x+x)^{2/x}	\lim\:_{x\to\:0}((e^{x}+x)^{\frac{2}{x}})
integral from-1 to 0 of sqrt(3u+4)	\int\:_{-1}^{0}\sqrt{3u+4}du
integral of x^9sqrt(x^5+5)	\int\:x^{9}\sqrt{x^{5}+5}dx
derivative of (7x^2-14x+14e^x)	\frac{d}{dx}((7x^{2}-14x+14)e^{x})
integral of 1/((x-1)(x-2)(x-3))	\int\:\frac{1}{(x-1)(x-2)(x-3)}dx
derivative of-(30/(x^4))	\frac{d}{dx}(-\frac{30}{x^{4}})
integral of (1-2x^2+3x^3)	\int\:(1-2x^{2}+3x^{3})dx
laplacetransform e^{-t}*sin(2t)	laplacetransform\:e^{-t}\cdot\:\sin(2t)
f(x)=-sin(2x)*2	f(x)=-\sin(2x)\cdot\:2
integral of x/(e^{-x^2)}	\int\:\frac{x}{e^{-x^{2}}}dx
(\partial)/(\partial x)(2xln(y))	\frac{\partial\:}{\partial\:x}(2x\ln(y))
derivative of 2x^2-e^x	\frac{d}{dx}(2x^{2}-e^{x})

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