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Popular Calculus Problems

area (x)^{(1/2)},-x^2,0,(1)	area\:(x)^{(\frac{1}{2})},-x^{2},0,(1)
integral of 10xsqrt(x)	\int\:10x\sqrt{x}dx
integral of (-1(x-9))/((x+5)(x-2))	\int\:\frac{-1(x-9)}{(x+5)(x-2)}dx
y^'+xy=-x^3	y^{\prime\:}+xy=-x^{3}
(d^2)/(dx^2)(x^5e^x)	\frac{d^{2}}{dx^{2}}(x^{5}e^{x})
derivative of y=7sqrt(x)	derivative\:y=7\sqrt{x}
limit as x approaches-infinity of 3^x	\lim\:_{x\to\:-\infty\:}(3^{x})
limit as x approaches 2 of-((x+3)/(x-2))	\lim\:_{x\to\:2}(-(\frac{x+3}{x-2}))
integral of+(sin^2(1/t))/(t^2)	\int\:+\frac{\sin^{2}(\frac{1}{t})}{t^{2}}dt
sum from n=1 to infinity of (n!)/(n3^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{n3^{n}}
(\partial)/(\partial z)(x^2+y^2-z)	\frac{\partial\:}{\partial\:z}(x^{2}+y^{2}-z)
derivative of (5tan(x)/x)	\frac{d}{dx}(\frac{5\tan(x)}{x})
integral of 7/(5y-105)	\int\:\frac{7}{5y-105}dy
(\partial)/(\partial x)(x^2+xy-25)	\frac{\partial\:}{\partial\:x}(x^{2}+xy-25)
integral from a to 2a of x	\int\:_{a}^{2a}xdx
integral of t^2-4	\int\:t^{2}-4dt
derivative of x+x^3	\frac{d}{dx}(x+x^{3})
derivative of 2sqrt(x)+1/(3x^3)	\frac{d}{dx}(2\sqrt{x}+\frac{1}{3x^{3}})
taylor x+(x^3)/3-tan(x)	taylor\:x+\frac{x^{3}}{3}-\tan(x)
limit as x approaches infinity of ((e^x+e^{-x}))/2	\lim\:_{x\to\:\infty\:}(\frac{(e^{x}+e^{-x})}{2})
derivative of x^2arctan(2x)	\frac{d}{dx}(x^{2}\arctan(2x))
derivative of 4sin(x-4xcos(x))	\frac{d}{dx}(4\sin(x)-4x\cos(x))
sum from n=3 to infinity of 1/(n^2+3n)	\sum\:_{n=3}^{\infty\:}\frac{1}{n^{2}+3n}
(\partial)/(\partial x)(sqrt(5x+y))	\frac{\partial\:}{\partial\:x}(\sqrt{5x+y})
limit as x approaches-1 of x/(x^2+x)	\lim\:_{x\to\:-1}(\frac{x}{x^{2}+x})
derivative of f(x)=e^{x^2-6}	derivative\:f(x)=e^{x^{2}-6}
limit as x approaches 0 of x*(ln(x))^2	\lim\:_{x\to\:0}(x\cdot\:(\ln(x))^{2})
(\partial)/(\partial x)(2sin(2x)cos(2y))	\frac{\partial\:}{\partial\:x}(2\sin(2x)\cos(2y))
(\partial)/(\partial x)(1/(x+1))	\frac{\partial\:}{\partial\:x}(\frac{1}{x+1})
derivative of 2(sqrt(x))+1	derivative\:2(\sqrt{x})+1
area-7x^2+63,-x^2+9	area\:-7x^{2}+63,-x^{2}+9
limit as x approaches-1 of (1-x^2)/(x+1)	\lim\:_{x\to\:-1}(\frac{1-x^{2}}{x+1})
derivative of f(x)=x^{1/5}	derivative\:f(x)=x^{\frac{1}{5}}
simplify (x+1)/(sqrt(x^2+1))	simplify\:\frac{x+1}{\sqrt{x^{2}+1}}
((dy)/(dx))=(((x-y^2))/((2xy+y)))	(\frac{dy}{dx})=(\frac{(x-y^{2})}{(2xy+y)})
integral of (x-arctan(x))/(1+x^2)	\int\:\frac{x-\arctan(x)}{1+x^{2}}dx
d/(dy)(-y/((x+2)^2))	\frac{d}{dy}(-\frac{y}{(x+2)^{2}})
derivative of ln(3x-e^{sec(x)})	\frac{d}{dx}(\ln(3x)-e^{\sec(x)})
f(x)=(sqrt(x+1))/(x^2-5)	f(x)=\frac{\sqrt{x+1}}{x^{2}-5}
f(t)=e^tcos(t)	f(t)=e^{t}\cos(t)
maclaurin sin(3x+2)	maclaurin\:\sin(3x+2)
limit as x approaches 0 of sin(1/x)x	\lim\:_{x\to\:0}(\sin(\frac{1}{x})x)
derivative of-0.4x^2+1000	\frac{d}{dx}(-0.4x^{2}+1000)
(\partial)/(\partial y)(xy-3xz+yz)	\frac{\partial\:}{\partial\:y}(xy-3xz+yz)
integral of (x^5)/(sqrt(x^2+8))	\int\:\frac{x^{5}}{\sqrt{x^{2}+8}}dx
limit as x approaches 3 of (-x)/(x-3)	\lim\:_{x\to\:3}(\frac{-x}{x-3})
limit as x approaches 0+of (tan(2x))^x	\lim\:_{x\to\:0+}((\tan(2x))^{x})
derivative of 1+sqrt(x^3)	\frac{d}{dx}(1+\sqrt{x^{3}})
derivative of (x^2+x^3/(x^2))	\frac{d}{dx}(\frac{x^{2}+x^{3}}{x^{2}})
derivative of picos(x)	\frac{d}{dx}(π\cos(x))
area e^x,e^{-3x},x=ln(5)	area\:e^{x},e^{-3x},x=\ln(5)
integral of (x+5)/(x^2+9)	\int\:\frac{x+5}{x^{2}+9}dx
derivative of 1/(x-8)	derivative\:\frac{1}{x-8}
integral of (6x^3+2x^2-45x-15)/(x^2-9)	\int\:\frac{6x^{3}+2x^{2}-45x-15}{x^{2}-9}dx
derivative of sqrt(6-x)	derivative\:\sqrt{6-x}
sum from n=0 to infinity of (n^2)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{n^{2}}{2^{n}}
derivative of xsin(6/x)	\frac{d}{dx}(x\sin(\frac{6}{x}))
area y=(x^2)/2-3,y=-(x^2)/2+2x	area\:y=\frac{x^{2}}{2}-3,y=-\frac{x^{2}}{2}+2x
integral from 1 to 9 of 1/(x-7)	\int\:_{1}^{9}\frac{1}{x-7}dx
derivative of-xe^{((x+1/(x-1))})	\frac{d}{dx}(-xe^{(\frac{x+1}{x-1})})
integral of (x^2)/(x^2-4x+5)	\int\:\frac{x^{2}}{x^{2}-4x+5}dx
derivative of x+5e^x	\frac{d}{dx}(x+5e^{x})
tangent of sqrt(x)(49.7)	tangent\:\sqrt{x}(49.7)
derivative of (x^2+1e^{x-1})	\frac{d}{dx}((x^{2}+1)e^{x-1})
y^{''}+3y^'=0,y(0)=7,y^'(0)=-3	y^{\prime\:\prime\:}+3y^{\prime\:}=0,y(0)=7,y^{\prime\:}(0)=-3
x(dy)/(dx)+(3x+1)y=e^{-3x}	x\frac{dy}{dx}+(3x+1)y=e^{-3x}
derivative of 3sqrt(2x-5)	\frac{d}{dx}(3\sqrt{2x-5})
derivative of 1/(1+4x^2-arctan(2x))	\frac{d}{dx}(\frac{1}{1+4x^{2}}-\arctan(2x))
laplacetransform e^{-t}sin^2(t)	laplacetransform\:e^{-t}\sin^{2}(t)
xy^{'''}-2/x y^'=0	xy^{\prime\:\prime\:\prime\:}-\frac{2}{x}y^{\prime\:}=0
derivative of sin({p}(x)ix)	\frac{d}{dx}(\sin({p}(x))ix)
derivative of cos(8x)	derivative\:\cos(8x)
inverse oflaplace s/((s-3)^2)	inverselaplace\:\frac{s}{(s-3)^{2}}
integral of (x^2+x)^{13}(2x+1)	\int\:(x^{2}+x)^{13}(2x+1)dx
integral of (t)^{1/2}	\int\:(t)^{\frac{1}{2}}dt
integral of sqrt(tan(6x))(sec(6x))^2	\int\:\sqrt{\tan(6x)}(\sec(6x))^{2}dx
integral of 8sin(sqrt(x))	\int\:8\sin(\sqrt{x})dx
d/(dy)(1-3/y+x)	\frac{d}{dy}(1-\frac{3}{y}+x)
(dy)/(dx)=-y^2sin(x)	\frac{dy}{dx}=-y^{2}\sin(x)
integral of 1/(x(x^2-49)^{3/2)}	\int\:\frac{1}{x(x^{2}-49)^{\frac{3}{2}}}dx
(y^2+yx)dx-x^2dy=0	(y^{2}+yx)dx-x^{2}dy=0
integral of (x^2+1)sin(x)	\int\:(x^{2}+1)\sin(x)dx
integral of x\sqrt[3]{x+4}	\int\:x\sqrt[3]{x+4}dx
integral from 1 to 3 of xsqrt(x^2+1)	\int\:_{1}^{3}x\sqrt{x^{2}+1}dx
d/(dy)(3)	\frac{d}{dy}(3)
derivative of xsqrt(5-x)	\frac{d}{dx}(x\sqrt{5-x})
derivative of (cos(t))/t	derivative\:\frac{\cos(t)}{t}
integral of e^{(3x)}	\int\:e^{(3x)}dx
integral of (x+3)/((x-2)(x+5))	\int\:\frac{x+3}{(x-2)(x+5)}dx
(\partial)/(\partial x)((x-1)^{2/3}(y^2-4))	\frac{\partial\:}{\partial\:x}((x-1)^{\frac{2}{3}}(y^{2}-4))
(\partial)/(\partial y)(y(x+y+1))	\frac{\partial\:}{\partial\:y}(y(x+y+1))
derivative of (x-5^3)	\frac{d}{dx}((x-5)^{3})
integral of 1/((x^2-2x+2)^2)	\int\:\frac{1}{(x^{2}-2x+2)^{2}}dx
integral of 4/(1-x^2)	\int\:\frac{4}{1-x^{2}}dx
derivative of (4x^3-2x+1/(x^2))	\frac{d}{dx}(\frac{4x^{3}-2x+1}{x^{2}})
integral from 0 to 2pi of 3sin(2x)	\int\:_{0}^{2π}3\sin(2x)dx
limit as x approaches 0 of (-ln(1+6x))/x	\lim\:_{x\to\:0}(\frac{-\ln(1+6x)}{x})
integral of (x^3)/(sqrt(1+x^2-x^4))	\int\:\frac{x^{3}}{\sqrt{1+x^{2}-x^{4}}}dx
d/(dy)((xy)/(x^2+y^2))	\frac{d}{dy}(\frac{xy}{x^{2}+y^{2}})
derivative of f(x)=(2-5x)/(e^x)	derivative\:f(x)=\frac{2-5x}{e^{x}}

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