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Popular Calculus Problems

derivative of f(x)=csc^7(2x^pi+pi^3)	derivative\:f(x)=\csc^{7}(2x^{π}+π^{3})
y^{''}-9y=0	y^{\prime\:\prime\:}-9y=0
integral of 1/((x+5)^2(x-3))	\int\:\frac{1}{(x+5)^{2}(x-3)}dx
sum from n=2 to infinity of ((3x-2)^n)/n	\sum\:_{n=2}^{\infty\:}\frac{(3x-2)^{n}}{n}
derivative of y=sin(2t)	derivative\:y=\sin(2t)
integral of 4cos^4(5x)	\int\:4\cos^{4}(5x)dx
f(x)=(e^x)/(1+e^x)	f(x)=\frac{e^{x}}{1+e^{x}}
integral from 1 to 2 of x^{-2}	\int\:_{1}^{2}x^{-2}dx
area y=(16)/(x^2-6x-55),x=-3,x=3	area\:y=\frac{16}{x^{2}-6x-55},x=-3,x=3
integral of (x^2+132x+132)/(x^3-4x)	\int\:\frac{x^{2}+132x+132}{x^{3}-4x}dx
integral of x/(3x^2-1)	\int\:\frac{x}{3x^{2}-1}dx
integral of 7x^2y+3/x-1	\int\:7x^{2}y+\frac{3}{x}-1dx
(dx)/(dy)=3x(5-x)	\frac{dx}{dy}=3x(5-x)
(3t+6y+3)=(dy)/(dt)	(3t+6y+3)=\frac{dy}{dt}
derivative of x	derivative\:x
limit as x approaches+0 of arctan(x)	\lim\:_{x\to\:+0}(\arctan(x))
derivative of 7/(\sqrt[3]{x})	\frac{d}{dx}(\frac{7}{\sqrt[3]{x}})
integral of sin(x)cos^4(x	\int\:\sin(x)\cos^{4}(d)xdx
sum from n=1 to infinity of (cos(1))^n	\sum\:_{n=1}^{\infty\:}(\cos(1))^{n}
du= 1/(2sqrt(x))dx	du=\frac{1}{2\sqrt{x}}dx
integral of e^{3x}cos(5x)	\int\:e^{3x}\cos(5x)dx
taylor cos(x),\at pi/2	taylor\:\cos(x),\at\:\frac{π}{2}
derivative of f(x)=2x^3-21x^2+72x-5	derivative\:f(x)=2x^{3}-21x^{2}+72x-5
(\partial)/(\partial x)(e^{2x-y})	\frac{\partial\:}{\partial\:x}(e^{2x-y})
integral of-30t^{2/3}	\int\:-30t^{\frac{2}{3}}dt
inverse oflaplace s/(2(s^2+4s+6))	inverselaplace\:\frac{s}{2(s^{2}+4s+6)}
limit as x approaches 4 of (3x^2-8x-16)/(2x^2-9x+4)	\lim\:_{x\to\:4}(\frac{3x^{2}-8x-16}{2x^{2}-9x+4})
integral of x(x-3)^2+4^2	\int\:x(x-3)^{2}+4^{2}dx
area y=x^2,y=x+2,x=-2	area\:y=x^{2},y=x+2,x=-2
maclaurin ln(1/(x+5))+xcos(x)	maclaurin\:\ln(\frac{1}{x+5})+x\cos(x)
integral of sin(6pit)	\int\:\sin(6πt)dt
derivative of 5-5cos(x)	\frac{d}{dx}(5-5\cos(x))
integral of \sqrt[3]{2-3x}	\int\:\sqrt[3]{2-3x}dx
derivative of 1/((x^2+1^4))	\frac{d}{dx}(\frac{1}{(x^{2}+1)^{4}})
(\partial)/(\partial y)(-2xy)	\frac{\partial\:}{\partial\:y}(-2xy)
sin(t)=y^'+y	\sin(t)=y^{\prime\:}+y
sum from n=1 to infinity of (-1)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{-1}{n+1}
limit as n approaches infinity of 7^n	\lim\:_{n\to\:\infty\:}(7^{n})
integral from 0 to 11 of 2piy(121-y^2)	\int\:_{0}^{11}2πy(121-y^{2})dy
limit as x approaches 0 of e^{2pi}	\lim\:_{x\to\:0}(e^{2π})
integral of (35x^4-3)/(7x^5-3x)	\int\:\frac{35x^{4}-3}{7x^{5}-3x}dx
integral of (x^2-4x-15)	\int\:(x^{2}-4x-15)dx
integral of x^2cos(4x)	\int\:x^{2}\cos(4x)dx
integral of sqrt(x+y)	\int\:\sqrt{x+y}dx
integral of (3x^2y)	\int\:(3x^{2}y)dx
y^'=(x^8-8y)/x	y^{\prime\:}=\frac{x^{8}-8y}{x}
x(dy)/(dx)+2y=-3sin(x)	x\frac{dy}{dx}+2y=-3\sin(x)
y^{''}+2y^'+5y=10	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=10
limit as x approaches 4 of (x^2-9)/(x-3)	\lim\:_{x\to\:4}(\frac{x^{2}-9}{x-3})
area (sec^2(x))/2 ,2cos^2(x)	area\:\frac{\sec^{2}(x)}{2},2\cos^{2}(x)
limit as x approaches 0 of 1/(sqrt(5)+\sqrt{5)}	\lim\:_{x\to\:0}(\frac{1}{\sqrt{5}+\sqrt{5}})
(dy)/(dx)+2y=1	\frac{dy}{dx}+2y=1
(dy)/(dx)+3x^2*y=6x^2	\frac{dy}{dx}+3x^{2}\cdot\:y=6x^{2}
(\partial)/(\partial y)(arctan(xy))	\frac{\partial\:}{\partial\:y}(\arctan(xy))
integral of cos(x)tan^2(x)	\int\:\cos(x)\tan^{2}(x)dx
integral of \sqrt[4]{x^3}	\int\:\sqrt[4]{x^{3}}dx
derivative of x=6.4cos(1.2^2t^2)	derivative\:x=6.4\cos(1.2^{2}t^{2})
integral of sin(4x)sin(3x)	\int\:\sin(4x)\sin(3x)dx
y^{''}+4y^'+3y=6e^{-x}	y^{\prime\:\prime\:}+4y^{\prime\:}+3y=6e^{-x}
integral of 1/(sqrt(ax+b))	\int\:\frac{1}{\sqrt{ax+b}}dx
derivative of y=ln(x^2+y^2)	derivative\:y=\ln(x^{2}+y^{2})
(\partial)/(\partial y)(e^{x^2-y^2})	\frac{\partial\:}{\partial\:y}(e^{x^{2}-y^{2}})
derivative of x*sqrt(9-x)	\frac{d}{dx}(x\cdot\:\sqrt{9-x})
integral from 4 to 4 of f(x)	\int\:_{4}^{4}f(x)dx
integral of (3e^x)	\int\:(3e^{x})dx
tangent of 6/(x^2+4)	tangent\:\frac{6}{x^{2}+4}
(\partial)/(\partial x)(4pi^2 y/(x^2))	\frac{\partial\:}{\partial\:x}(4π^{2}\frac{y}{x^{2}})
derivative of arctan(2x)	derivative\:\arctan(2x)
limit as x approaches 0 of (2x)/0	\lim\:_{x\to\:0}(\frac{2x}{0})
area e^x,x,0,2	area\:e^{x},x,0,2
limit as x approaches-4 of-8/(x^2+8x+16)	\lim\:_{x\to\:-4}(-\frac{8}{x^{2}+8x+16})
limit as x approaches 0 of (1-5x)^{4/x}	\lim\:_{x\to\:0}((1-5x)^{\frac{4}{x}})
limit as x approaches-2 of (x-1)/(3x+6)	\lim\:_{x\to\:-2}(\frac{x-1}{3x+6})
limit as x approaches 4 of \sqrt[3]{x+4}	\lim\:_{x\to\:4}(\sqrt[3]{x+4})
(y^4-x^2)*(dy)/(dx)=-xy	(y^{4}-x^{2})\cdot\:\frac{dy}{dx}=-xy
integral of (x-1)^5	\int\:(x-1)^{5}dx
laplacetransform e^{-t}cos(2t)	laplacetransform\:e^{-t}\cos(2t)
(\partial)/(\partial x)(x^{1/2}y^{1/2}z)	\frac{\partial\:}{\partial\:x}(x^{\frac{1}{2}}y^{\frac{1}{2}}z)
integral from 0 to 6 of sqrt(1+x)	\int\:_{0}^{6}\sqrt{1+x}dx
limit as x approaches 3+of (x+9)/(x-3)	\lim\:_{x\to\:3+}(\frac{x+9}{x-3})
derivative of (2x^2+4x/(2+x^2))	\frac{d}{dx}(\frac{2x^{2}+4x}{2+x^{2}})
f(x)=ln(3x+2)	f(x)=\ln(3x+2)
derivative of (24)/(x^2+12)	derivative\:\frac{24}{x^{2}+12}
derivative of xsqrt(3600-x^2)	derivative\:x\sqrt{3600-x^{2}}
derivative of ((x^2+3/(x^2-3))^2)	\frac{d}{dx}((\frac{x^{2}+3}{x^{2}-3})^{2})
integral of 1/(sqrt(x)\sqrt{1+x)}	\int\:\frac{1}{\sqrt{x}\sqrt{1+x}}dx
integral of e^{sqrt(3x+9)}	\int\:e^{\sqrt{3x+9}}dx
derivative of e^{-2x^3+2}	\frac{d}{dx}(e^{-2x^{3}+2})
integral of 1/(x^{1.00001)}	\int\:\frac{1}{x^{1.00001}}dx
integral of 1/(sqrt((4-x^2)^3))	\int\:\frac{1}{\sqrt{(4-x^{2})^{3}}}dx
limit as x approaches infinity of 1.01^x	\lim\:_{x\to\:\infty\:}(1.01^{x})
(x^2-x+1)y^{''}-(x^2+x)y^'+(x+1)y=0	(x^{2}-x+1)y^{\prime\:\prime\:}-(x^{2}+x)y^{\prime\:}+(x+1)y=0
maclaurin 6sin(x)	maclaurin\:6\sin(x)
(\partial)/(\partial x)(x(y)^{1/2})	\frac{\partial\:}{\partial\:x}(x(y)^{\frac{1}{2}})
derivative of y=(x^5)/(10)+1/(6x^3)	derivative\:y=\frac{x^{5}}{10}+\frac{1}{6x^{3}}
d/(dt)(4e^{2t})	\frac{d}{dt}(4e^{2t})
integral of (e^{4x})/(e^{4x)+1}	\int\:\frac{e^{4x}}{e^{4x}+1}dx
derivative of 7e^{-3x}	\frac{d}{dx}(7e^{-3x})
integral of cos^6(x)	\int\:\cos^{6}(x)dx
integral of sin(4t)	\int\:\sin(4t)dt

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