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Popular Calculus Problems

d/(dt)({p}(t)e^t)	\frac{d}{dt}({p}(t)e^{t})
normal of y=5+sqrt(1-x),(-8,8)	normal\:y=5+\sqrt{1-x},(-8,8)
integral from 0 to 12 of 2piy(144-y^2)	\int\:_{0}^{12}2πy(144-y^{2})dy
integral of cos(x)sec(x)sin(x)	\int\:\cos(x)\sec(x)\sin(x)dx
derivative of 1+xe^x	\frac{d}{dx}(1+xe^{x})
inverse oflaplace (3s+2)/((s+1)^3)	inverselaplace\:\frac{3s+2}{(s+1)^{3}}
integral from-1 to 3 of (x^3+1)	\int\:_{-1}^{3}(x^{3}+1)dx
limit as t approaches 1 of sqrt(t+1)	\lim\:_{t\to\:1}(\sqrt{t+1})
integral from 7 to infinity of 9/(v^2-v)	\int\:_{7}^{\infty\:}\frac{9}{v^{2}-v}dv
limit as x approaches 2+of (\|2-x\|)/(2-x)	\lim\:_{x\to\:2+}(\frac{\left\|2-x\right\|}{2-x})
(\partial)/(\partial x)(1/(sqrt(x^2)))	\frac{\partial\:}{\partial\:x}(\frac{1}{\sqrt{x^{2}}})
derivative of (x^3-3)/(x^2+2)	derivative\:\frac{x^{3}-3}{x^{2}+2}
integral from 1 to 5 of x	\int\:_{1}^{5}xdx
integral of x^2(ln(x))^2	\int\:x^{2}(\ln(x))^{2}dx
derivative of y=-6x	derivative\:y=-6x
integral of (2/(x^3)+sqrt(x^4))	\int\:(\frac{2}{x^{3}}+\sqrt{x^{4}})dx
derivative of ln(tan(2x))	\frac{d}{dx}(\ln(\tan(2x)))
(\partial)/(\partial t)(1-cos(t))	\frac{\partial\:}{\partial\:t}(1-\cos(t))
derivative of 8/(x^7)	\frac{d}{dx}(\frac{8}{x^{7}})
integral of (x^2+4x+1)/(x+3)	\int\:\frac{x^{2}+4x+1}{x+3}dx
integral from 0 to 1 of t^3(1+t^4)^3	\int\:_{0}^{1}t^{3}(1+t^{4})^{3}dt
tangent of f(x)=7x-sqrt(x),(4,26)	tangent\:f(x)=7x-\sqrt{x},(4,26)
derivative of (2sin(x)/(sec(x)))	\frac{d}{dx}(\frac{2\sin(x)}{\sec(x)})
inverse oflaplace 2/((s-4)^2)	inverselaplace\:\frac{2}{(s-4)^{2}}
derivative of 1/(1+e^{1/x})	\frac{d}{dx}(\frac{1}{1+e^{\frac{1}{x}}})
limit as x approaches 3-of (\|x\|)/x	\lim\:_{x\to\:3-}(\frac{\left\|x\right\|}{x})
-xy+(3+x)((dy)/(dx))=0	-xy+(3+x)(\frac{dy}{dx})=0
sum from n=1 to infinity of 8(0.8)^{n-1}	\sum\:_{n=1}^{\infty\:}8(0.8)^{n-1}
integral of (5x^2-3x+2)/(x^3-2x^2)	\int\:\frac{5x^{2}-3x+2}{x^{3}-2x^{2}}dx
y^'=(y+sqrt(x^2-y^2))/x	y^{\prime\:}=\frac{y+\sqrt{x^{2}-y^{2}}}{x}
derivative of acos(x)	\frac{d}{dx}(a\cos(x))
derivative of (x-1/x+ln(x))	\frac{d}{dx}(\frac{x-1}{x}+\ln(x))
dy=xsqrt(y)dx	dy=x\sqrt{y}dx
integral of 8/((x+2)(x^2+4))	\int\:\frac{8}{(x+2)(x^{2}+4)}dx
tangent of (-5x^2)/(2x+3)	tangent\:\frac{-5x^{2}}{2x+3}
derivative of arcsin(a/x)	\frac{d}{dx}(\arcsin(\frac{a}{x}))
integral of (x^3-2x^2+5x-2)/(x^3-2x^2+x)	\int\:\frac{x^{3}-2x^{2}+5x-2}{x^{3}-2x^{2}+x}dx
derivative of-2sin^2(x)	\frac{d}{dx}(-2\sin^{2}(x))
sum from n=1 to infinity of ((ln(3n)))/n	\sum\:_{n=1}^{\infty\:}\frac{(\ln(3n))}{n}
derivative of (2x-3)^6	derivative\:(2x-3)^{6}
expand \sqrt[3]{x}(2+x)	expand\:\sqrt[3]{x}(2+x)
limit as x approaches 0+of e^{cot(x)}	\lim\:_{x\to\:0+}(e^{\cot(x)})
(y-b)*y^'+x-a=0	(y-b)\cdot\:y^{\prime\:}+x-a=0
(\partial)/(\partial y)(x^3-xy)	\frac{\partial\:}{\partial\:y}(x^{3}-xy)
limit as x approaches 6 of x^2	\lim\:_{x\to\:6}(x^{2})
limit as x approaches 0 of x/(sin(9x))	\lim\:_{x\to\:0}(\frac{x}{\sin(9x)})
(2dy)/(dx)-4xy=8x,y(0)=15	\frac{2dy}{dx}-4xy=8x,y(0)=15
derivative of ln((1+x^2/(1-x^2)))	\frac{d}{dx}(\ln(\frac{1+x^{2}}{1-x^{2}}))
(\partial)/(\partial x)(e^{2x}-xcos(t))	\frac{\partial\:}{\partial\:x}(e^{2x}-x\cos(t))
derivative of f(x)= 1/(x^2)	derivative\:f(x)=\frac{1}{x^{2}}
derivative of x^3-3x^2+4	\frac{d}{dx}(x^{3}-3x^{2}+4)
integral of 1/(csc(5x)sqrt(cos(5x)))	\int\:\frac{1}{\csc(5x)\sqrt{\cos(5x)}}dx
derivative of e^{2x+y}	\frac{d}{dx}(e^{2x+y})
integral of (x^4-5e^{-2x})	\int\:(x^{4}-5e^{-2x})dx
x(dy)/(dx)+y=x,y(1)=3	x\frac{dy}{dx}+y=x,y(1)=3
integral from 0 to (3pi)/2 of cos^3(37x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(37x)dx
integral of (cos(x))/(sqrt((1-sin(x))))	\int\:\frac{\cos(x)}{\sqrt{(1-\sin(x))}}dx
area 8x^2-x^3,x^2+11x,0,5	area\:8x^{2}-x^{3},x^{2}+11x,0,5
integral of sin^2(4x)	\int\:\sin^{2}(4x)dx
d/(dy)(sqrt(10y-y^2))	\frac{d}{dy}(\sqrt{10y-y^{2}})
(\partial)/(\partial y)(x^{y-1})	\frac{\partial\:}{\partial\:y}(x^{y-1})
x((dy)/(dx))+2y=3	x(\frac{dy}{dx})+2y=3
(\partial)/(\partial y)(2/y)	\frac{\partial\:}{\partial\:y}(\frac{2}{y})
derivative of f(x)=2sec(x)tan(x)	derivative\:f(x)=2\sec(x)\tan(x)
integral of ((6+e^x)^2)/(e^x)	\int\:\frac{(6+e^{x})^{2}}{e^{x}}dx
f(x)=e^{sqrt(x)}+ln(x+1)	f(x)=e^{\sqrt{x}}+\ln(x+1)
simplify 6x^2+(768)/x	simplify\:6x^{2}+\frac{768}{x}
limit as x approaches+1 of (-1)/(x-1)	\lim\:_{x\to\:+1}(\frac{-1}{x-1})
derivative of (ln(x^3+1)/(2^{x^4)-6})	\frac{d}{dx}(\frac{\ln(x^{3}+1)}{2^{x^{4}}-6})
integral of 1/(1-u)	\int\:\frac{1}{1-u}du
integral of e^{7x+8}	\int\:e^{7x+8}dx
derivative of ln(tan^2(x))	derivative\:\ln(\tan^{2}(x))
area y=x,y=x^2-2,y=0	area\:y=x,y=x^{2}-2,y=0
sum from n=0 to infinity of e^{(2n-1)}	\sum\:_{n=0}^{\infty\:}e^{(2n-1)}
integral of (2x+1)/(x^2-x+3)	\int\:\frac{2x+1}{x^{2}-x+3}dx
limit as x approaches 2 of 8/x	\lim\:_{x\to\:2}(\frac{8}{x})
integral from 9 to infinity of 2/(x^3)	\int\:_{9}^{\infty\:}\frac{2}{x^{3}}dx
(ye^{xy}-1/y)dx(xe^{xy}-x/(y^2))dy=0	(ye^{xy}-\frac{1}{y})dx(xe^{xy}-\frac{x}{y^{2}})dy=0
derivative of f(x)=(5t+300)/(t^2+25)	derivative\:f(x)=\frac{5t+300}{t^{2}+25}
integral of x^2y^2	\int\:x^{2}y^{2}dx
derivative of (-7x^2+7)^5(-7x^2+4)^{-4}	derivative\:(-7x^{2}+7)^{5}(-7x^{2}+4)^{-4}
integral of (\sqrt[5]{x^2})	\int\:(\sqrt[5]{x^{2}})dx
integral from 1 to 2 of (x^4)/8+1/(4x^2)	\int\:_{1}^{2}\frac{x^{4}}{8}+\frac{1}{4x^{2}}dx
integral of (-x^2cos(y)sin(y)-xcos(y))	\int\:(-x^{2}\cos(y)\sin(y)-x\cos(y))dy
(((x+1))/((x+1)^2+4))^'	(\frac{(x+1)}{(x+1)^{2}+4})^{\prime\:}
derivative of (x^5-6/x ^{-2})	\frac{d}{dx}((x^{5}-\frac{6}{x})^{-2})
integral from 0 to 1 of xe^x	\int\:_{0}^{1}xe^{x}dx
slope of (2.6)(-3.5)	slope\:(2.6)(-3.5)
derivative of 4sin(3x)	derivative\:4\sin(3x)
(dy)/(dx)+x^2(3y-2)=0	\frac{dy}{dx}+x^{2}(3y-2)=0
derivative of sqrt(((1-x)/(1+x)))	\frac{d}{dx}(\sqrt{\frac{(1-x)}{1+x}})
integral of (-4sin(2x)+3cos(3x))	\int\:(-4\sin(2x)+3\cos(3x))dx
derivative of (2x^5+6)/(x^3)	derivative\:\frac{2x^{5}+6}{x^{3}}
area x^2,x+2,2,-1	area\:x^{2},x+2,2,-1
integral of-5x^5e^{x^6}	\int\:-5x^{5}e^{x^{6}}dx
integral of 9x	\int\:9xdx
integral of 1/(e^x-9e^{-x)}	\int\:\frac{1}{e^{x}-9e^{-x}}dx
limit as x approaches 0 of (arctan(x))/x	\lim\:_{x\to\:0}(\frac{\arctan(x)}{x})
integral of (5x+4)/((x+8)^2(x-1))	\int\:\frac{5x+4}{(x+8)^{2}(x-1)}dx
(dy)/(dx)=(x-1)/(x+3)(y-2)/(y-3)	\frac{dy}{dx}=\frac{x-1}{x+3}\frac{y-2}{y-3}

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