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Popular Calculus Problems

integral of rcos(r^2)	\int\:r\cos(r^{2})dr
integral of ln(x^x)	\int\:\ln(x^{x})dx
integral of (4x^3+2x)	\int\:(4x^{3}+2x)dx
integral of 3(cos(x)+sin(2x))/(sin(x))	\int\:3\frac{\cos(x)+\sin(2x)}{\sin(x)}dx
limit as x approaches 0 of (1+x)^x	\lim\:_{x\to\:0}((1+x)^{x})
(\partial)/(\partial x)(xye^{3y})	\frac{\partial\:}{\partial\:x}(xye^{3y})
derivative of 10x^{1/5}	\frac{d}{dx}(10x^{\frac{1}{5}})
derivative of (x^2/(x+2))	\frac{d}{dx}(\frac{x^{2}}{x+2})
taylor x^{11/2},x=1	taylor\:x^{\frac{11}{2}},x=1
tangent of f(x)=-3x^{3/2}-1,\at x=4	tangent\:f(x)=-3x^{\frac{3}{2}}-1,\at\:x=4
derivative of f(x)=e^{1-2x}(x+cos(2x))	derivative\:f(x)=e^{1-2x}(x+\cos(2x))
area f(x)=x^3+x^2+1,g(x)=2x+1	area\:f(x)=x^{3}+x^{2}+1,g(x)=2x+1
integral of 1/(25-36x^2)	\int\:\frac{1}{25-36x^{2}}dx
sum from n=4 to infinity of e^{5-6n}	\sum\:_{n=4}^{\infty\:}e^{5-6n}
(\partial)/(\partial y)(y(1+ln(xy)))	\frac{\partial\:}{\partial\:y}(y(1+\ln(xy)))
ty^'+ty=1-y,y(1)=0	ty^{\prime\:}+ty=1-y,y(1)=0
integral of 1/(x-1)	\int\:\frac{1}{x-1}dx
derivative of (x^3-5x)(4x^2-3x)	derivative\:(x^{3}-5x)(4x^{2}-3x)
laplacetransform x+k*x	laplacetransform\:x+k\cdot\:x
derivative of (2-3x/(7-x))	\frac{d}{dx}(\frac{2-3x}{7-x})
integral of (e^xcos(y)-x-2)	\int\:(e^{x}\cos(y)-x-2)dy
integral of f^2(x)	\int\:f^{2}(x)dx
derivative of (2x-3^3)	\frac{d}{dx}((2x-3)^{3})
(\partial)/(\partial x)(4x+y)	\frac{\partial\:}{\partial\:x}(4x+y)
integral of 4e^{2x-1}	\int\:4e^{2x-1}dx
integral from-1 to 1 of 1/(sqrt(t+1))	\int\:_{-1}^{1}\frac{1}{\sqrt{t+1}}dt
(dy)/(dx)=42yx^6	\frac{dy}{dx}=42yx^{6}
integral from 0 to 1 of (2x+y)^8	\int\:_{0}^{1}(2x+y)^{8}dx
derivative of f(x)=x^3-3/2 x^2+4x+1	derivative\:f(x)=x^{3}-\frac{3}{2}x^{2}+4x+1
(x-4)y^'+y=x^2+8	(x-4)y^{\prime\:}+y=x^{2}+8
derivative of sqrt(3x^3)	derivative\:\sqrt{3x^{3}}
d/(dy)(ln(y))	\frac{d}{dy}(\ln(y))
area x=-2+4y,x=y^2+1	area\:x=-2+4y,x=y^{2}+1
(\partial)/(\partial x)(10xcos(4xy))	\frac{\partial\:}{\partial\:x}(10x\cos(4xy))
limit as x approaches 0 of ((x+1)^4-1)/x	\lim\:_{x\to\:0}(\frac{(x+1)^{4}-1}{x})
integral of xsin(x^2+4)	\int\:x\sin(x^{2}+4)dx
x(dy)/(dx)-2y=6x^5	x\frac{dy}{dx}-2y=6x^{5}
y^{''}+6y^'+9y=18t^2+24t+4	y^{\prime\:\prime\:}+6y^{\prime\:}+9y=18t^{2}+24t+4
derivative of f(x)= 1/(x+5)	derivative\:f(x)=\frac{1}{x+5}
integral from 0 to pi/2 of 5cos^2(x)	\int\:_{0}^{\frac{π}{2}}5\cos^{2}(x)dx
integral of (9x-4)/(x^3-4x^2)	\int\:\frac{9x-4}{x^{3}-4x^{2}}dx
integral from 1 to 6 of ln(x)	\int\:_{1}^{6}\ln(x)dx
d/(dt)(e^{a(e^t-1)})	\frac{d}{dt}(e^{a(e^{t}-1)})
y^{''}+3y^'+2y=7cos(x)-sin(x)	y^{\prime\:\prime\:}+3y^{\prime\:}+2y=7\cos(x)-\sin(x)
limit as x approaches a of ((\sqrt[3]{x})-\sqrt[3]{a})/(x^2-a^2)	\lim\:_{x\to\:a}(\frac{(\sqrt[3]{x})-\sqrt[3]{a}}{x^{2}-a^{2}})
(\partial)/(\partial z)(-z^2)	\frac{\partial\:}{\partial\:z}(-z^{2})
integral of (6x+5)/((9x^2+15x)^5)	\int\:\frac{6x+5}{(9x^{2}+15x)^{5}}dx
integral from 4 to 8 of t^3ln(5t)	\int\:_{4}^{8}t^{3}\ln(5t)dt
xy^'+2y=2cos(x)	xy^{\prime\:}+2y=2\cos(x)
derivative of (x^2-9x+1)/(x^2+5)	derivative\:\frac{x^{2}-9x+1}{x^{2}+5}
derivative of 5sin^2(t)	derivative\:5\sin^{2}(t)
derivative of 4xsin(x^2)	\frac{d}{dx}(4x\sin(x^{2}))
derivative of (2-x/(sqrt(1-y)))	\frac{d}{dx}(\frac{2-x}{\sqrt{1-y}})
(\partial)/(\partial x)(e^{-x/2})	\frac{\partial\:}{\partial\:x}(e^{-\frac{x}{2}})
integral of 1/4 sin(4x)	\int\:\frac{1}{4}\sin(4x)dx
slope of (-3,3),(4,-5)	slope\:(-3,3),(4,-5)
derivative of 9/(x+1)	derivative\:\frac{9}{x+1}
limit as x approaches-1 of (x+2)^7(2x)^2	\lim\:_{x\to\:-1}((x+2)^{7}(2x)^{2})
(\partial)/(\partial x)(3/(2x+3y))	\frac{\partial\:}{\partial\:x}(\frac{3}{2x+3y})
limit as x approaches-4 of (x+3)^2	\lim\:_{x\to\:-4}((x+3)^{2})
integral of x/(sqrt(x^2+x+1))	\int\:\frac{x}{\sqrt{x^{2}+x+1}}dx
derivative of-e^{3x}	\frac{d}{dx}(-e^{3x})
derivative of ((6x^2+2x+6))/(sqrt(x))	derivative\:\frac{(6x^{2}+2x+6)}{\sqrt{x}}
integral of r^2(r^3+6)^3	\int\:r^{2}(r^{3}+6)^{3}dr
(\partial)/(\partial x)(cos^9(x^7y^9))	\frac{\partial\:}{\partial\:x}(\cos^{9}(x^{7}y^{9}))
derivative of y=7arctan(x+sqrt(1+x^2))	derivative\:y=7\arctan(x+\sqrt{1+x^{2}})
area y=5x,y= 5/2 x,y=84-x^2	area\:y=5x,y=\frac{5}{2}x,y=84-x^{2}
derivative of 1/(\sqrt[6]{x})	\frac{d}{dx}(\frac{1}{\sqrt[6]{x}})
limit as x approaches 8 of ln(x-8)	\lim\:_{x\to\:8}(\ln(x-8))
integral from 1 to 10 of (25)/(x^3)	\int\:_{1}^{10}\frac{25}{x^{3}}dx
simplify e^{xy}	simplify\:e^{xy}
derivative of arctan(x+2y)	\frac{d}{dx}(\arctan(x+2y))
integral of x/(x^4+10x^2+26)	\int\:\frac{x}{x^{4}+10x^{2}+26}dx
limit as x approaches 0 of (2/3)^x	\lim\:_{x\to\:0}((\frac{2}{3})^{x})
integral of sin(3x)*sin(5x)	\int\:\sin(3x)\cdot\:\sin(5x)dx
limit as x approaches 0 of-2/x	\lim\:_{x\to\:0}(-\frac{2}{x})
derivative of 1/(5x-1)	\frac{d}{dx}(\frac{1}{5x-1})
derivative of arcsin(x^4)	derivative\:\arcsin(x^{4})
derivative of f(x)= 7/x	derivative\:f(x)=\frac{7}{x}
limit as x approaches infinity of ((x-3)/(x-4))^{-x}	\lim\:_{x\to\:\infty\:}((\frac{x-3}{x-4})^{-x})
derivative of ln(sinh(5x))	\frac{d}{dx}(\ln(\sinh(5x)))
derivative of y=(3x-2x^2)^3	derivative\:y=(3x-2x^{2})^{3}
derivative of (9+6x)/(7-4x)	derivative\:\frac{9+6x}{7-4x}
derivative of y=e^x(p+psqrt(p))	derivative\:y=e^{x}(p+p\sqrt{p})
maclaurin ln(2-3x)	maclaurin\:\ln(2-3x)
(dy}{dx}=\frac{xsec(y/x)+y)/x	\frac{dy}{dx}=\frac{x\sec(\frac{y}{x})+y}{x}
integral of sec(x/2)tan(x/2)	\int\:\sec(\frac{x}{2})\tan(\frac{x}{2})dx
derivative of y=2sqrt(5-x^2)	derivative\:y=2\sqrt{5-x^{2}}
integral of (x^2+3)^32x	\int\:(x^{2}+3)^{3}2xdx
(\partial)/(\partial x)(x^5y^5)	\frac{\partial\:}{\partial\:x}(x^{5}y^{5})
integral of (v+3)/(v-1)	\int\:\frac{v+3}{v-1}dv
derivative of 3(5-x^2)	\frac{d}{dx}(3(5-x)^{2})
(\partial)/(\partial z)(z^2cos(yx))	\frac{\partial\:}{\partial\:z}(z^{2}\cos(yx))
derivative of f(x)=(4t-1)(3t-6)^{-1}	derivative\:f(x)=(4t-1)(3t-6)^{-1}
integral of (x^2)/((x^3-6)^2)	\int\:\frac{x^{2}}{(x^{3}-6)^{2}}dx
derivative of f(x)= 1/(x^{10)}	derivative\:f(x)=\frac{1}{x^{10}}
tangent of f(x)=sqrt(x+7),(9,4)	tangent\:f(x)=\sqrt{x+7},(9,4)
(dx)/(dt)=(2x^2+tsqrt(7t^2+x^2))/(2tx)	\frac{dx}{dt}=\frac{2x^{2}+t\sqrt{7t^{2}+x^{2}}}{2tx}
derivative of f(x)=cos((e^x)/(x^4+1))	derivative\:f(x)=\cos(\frac{e^{x}}{x^{4}+1})
7t*(dy)/(dt)+y=sqrt(t)	7t\cdot\:\frac{dy}{dt}+y=\sqrt{t}

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