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Popular Calculus Problems

sum from n=1 to infinity of 3(1/5)^{n-1}	\sum\:_{n=1}^{\infty\:}3(\frac{1}{5})^{n-1}
derivative of f(x)=e^{2x}-1	derivative\:f(x)=e^{2x}-1
sum from n=1 to infinity of-n	\sum\:_{n=1}^{\infty\:}-n
limit as x approaches 0 of (sin(3x^2))/(ln(x^2+1))	\lim\:_{x\to\:0}(\frac{\sin(3x^{2})}{\ln(x^{2}+1)})
derivative of x/((x^2+y^2^{3/2)})	\frac{d}{dx}(\frac{x}{(x^{2}+y^{2})^{\frac{3}{2}}})
derivative of e^{tan(θ)}	derivative\:e^{\tan(θ)}
(\partial)/(\partial x)(yln(3x+5y))	\frac{\partial\:}{\partial\:x}(y\ln(3x+5y))
derivative of f(x)=e^{\sqrt[3]{x}}	derivative\:f(x)=e^{\sqrt[3]{x}}
area sqrt(x),2x-15,0	area\:\sqrt{x},2x-15,0
limit as x approaches 0 of x^4cos(7/x)	\lim\:_{x\to\:0}(x^{4}\cos(\frac{7}{x}))
integral from-1 to 1 of 7x^2-4x-3	\int\:_{-1}^{1}7x^{2}-4x-3dx
integral of (csc^2(x))/(sqrt(3-cot(x)))	\int\:\frac{\csc^{2}(x)}{\sqrt{3-\cot(x)}}dx
(\partial)/(\partial x)(-s^2t^2)	\frac{\partial\:}{\partial\:x}(-s^{2}t^{2})
t(dy)/(dt)+5y=t^3	t\frac{dy}{dt}+5y=t^{3}
integral of 1/(sqrt(8+2x-x^2))	\int\:\frac{1}{\sqrt{8+2x-x^{2}}}dx
limit as x approaches infinity of 8x^2	\lim\:_{x\to\:\infty\:}(8x^{2})
tangent of f(x)=5tan(x),\at x=1.57	tangent\:f(x)=5\tan(x),\at\:x=1.57
integral of (cos(t))^2	\int\:(\cos(t))^{2}dt
limit as x approaches 0 of (sin(3x))/(sin(6x))	\lim\:_{x\to\:0}(\frac{\sin(3x)}{\sin(6x)})
integral of 3e^x-9cos(x)+C	\int\:3e^{x}-9\cos(x)+Cdx
tangent of 4x^3	tangent\:4x^{3}
(dy)/(dx)=tan(x)+sec(x)	\frac{dy}{dx}=\tan(x)+\sec(x)
derivative of (cos(x))/(2sin(x))	derivative\:\frac{\cos(x)}{2\sin(x)}
(\partial)/(\partial v)(4usin(v))	\frac{\partial\:}{\partial\:v}(4u\sin(v))
integral of xsqrt(x-15)	\int\:x\sqrt{x-15}dx
integral of xe^{xy}	\int\:xe^{xy}dy
integral of e^{x+1}	\int\:e^{x+1}dx
derivative of 2/(x^2+4)	\frac{d}{dx}(\frac{2}{x^{2}+4})
derivative of f(t)=t^3e^{-2t}cos(6t)	derivative\:f(t)=t^{3}e^{-2t}\cos(6t)
(\partial)/(\partial x)(((x^2+y^2-4))/(xy))	\frac{\partial\:}{\partial\:x}(\frac{(x^{2}+y^{2}-4)}{xy})
taylor ln(3x+1),3	taylor\:\ln(3x+1),3
derivative of sqrt(4x^2+5)	\frac{d}{dx}(\sqrt{4x^{2}+5})
derivative of 1/((t^2+3t+1)^{5/2)}	derivative\:\frac{1}{(t^{2}+3t+1)^{\frac{5}{2}}}
derivative of y=x^4+8x^2-x	derivative\:y=x^{4}+8x^{2}-x
integral of 2x^3-2/3 x^2+7x	\int\:2x^{3}-\frac{2}{3}x^{2}+7xdx
sum from n=0 to infinity of 8/(4^n)	\sum\:_{n=0}^{\infty\:}\frac{8}{4^{n}}
(\partial)/(\partial x)(-sin(x^2y)x^2)	\frac{\partial\:}{\partial\:x}(-\sin(x^{2}y)x^{2})
integral of t*1/(e^t)	\int\:t\cdot\:\frac{1}{e^{t}}dt
integral of (-2sec(x)tan(x)-3sec^2(x))	\int\:(-2\sec(x)\tan(x)-3\sec^{2}(x))dx
5t*(dy)/(dt)+3y=sqrt(t)	5t\cdot\:\frac{dy}{dt}+3y=\sqrt{t}
(dx)/(dt)=((2t^2+x^2))/(tx)	\frac{dx}{dt}=\frac{(2t^{2}+x^{2})}{tx}
y^{''}-2y^'+5y=e^xsin(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+5y=e^{x}\sin(x)
integral from 0 to infinity of 1	\int\:_{0}^{\infty\:}1dx
integral of e^{-st}-te^{-st}	\int\:e^{-st}-te^{-st}dt
area y=x^3-x,y=3x	area\:y=x^{3}-x,y=3x
integral from-infinity to 0 of 1/(5-6x)	\int\:_{-\infty\:}^{0}\frac{1}{5-6x}dx
integral from 1 to 2 of (5-x)/(x^3)	\int\:_{1}^{2}\frac{5-x}{x^{3}}dx
derivative of (csc(x)^2)	\frac{d}{dx}((\csc(x))^{2})
sum from n=1 to infinity of e^{-8n}	\sum\:_{n=1}^{\infty\:}e^{-8n}
limit as t approaches pi of cos((2t)/3)	\lim\:_{t\to\:π}(\cos(\frac{2t}{3}))
derivative of 3/(x^2+10x^3-2sin(3x))	\frac{d}{dx}(\frac{3}{x^{2}}+10x^{3}-2\sin(3x))
integral of 8/(7+8x)	\int\:\frac{8}{7+8x}dx
area f(x)=-x^2+4,y+2x-4=0	area\:f(x)=-x^{2}+4,y+2x-4=0
derivative of sqrt(7-3x)	derivative\:\sqrt{7-3x}
integral from 1/2 to 2 of 1/(x^2)	\int\:_{\frac{1}{2}}^{2}\frac{1}{x^{2}}dx
area e^x,e^{4x},[0,1]	area\:e^{x},e^{4x},[0,1]
derivative of sqrt(x^3+2x)	derivative\:\sqrt{x^{3}+2x}
integral of 2/(e^{4x)}	\int\:\frac{2}{e^{4x}}dx
derivative of (2x/(1-cot(x)))	\frac{d}{dx}(\frac{2x}{1-\cot(x)})
integral of-sin^3(x)cos^2(x)	\int\:-\sin^{3}(x)\cos^{2}(x)dx
integral of (sqrt(y^2-144))/y	\int\:\frac{\sqrt{y^{2}-144}}{y}dy
derivative of f(x)=x^5cos(x)	derivative\:f(x)=x^{5}\cos(x)
integral of 1/(x(x^2+x+5))	\int\:\frac{1}{x(x^{2}+x+5)}dx
(\partial)/(\partial x)((6-x^2y^2)^2)	\frac{\partial\:}{\partial\:x}((6-x^{2}y^{2})^{2})
limit as x approaches 4+of (4+x)/(4-x)	\lim\:_{x\to\:4+}(\frac{4+x}{4-x})
limit as h approaches 0 of 6x+1+3h	\lim\:_{h\to\:0}(6x+1+3h)
inverse oflaplace {1/(s^2+s-20)}	inverselaplace\:\left\{\frac{1}{s^{2}+s-20}\right\}
derivative of arcsin(1-2x^2)	\frac{d}{dx}(\arcsin(1-2x^{2}))
derivative of e^x+x^2	\frac{d}{dx}(e^{x}+x^{2})
d/(dy)(ycos(x))	\frac{d}{dy}(y\cos(x))
(\partial)/(\partial x)(45-x^2-y^2)	\frac{\partial\:}{\partial\:x}(45-x^{2}-y^{2})
derivative of sin(2x-2pi)	\frac{d}{dx}(\sin(2x-2π))
integral of 1/(x^2+2x+5)	\int\:\frac{1}{x^{2}+2x+5}dx
(\partial)/(\partial x)(ln(x^6+1)+y^2)	\frac{\partial\:}{\partial\:x}(\ln(x^{6}+1)+y^{2})
derivative of 5/12 (3+sqrt(5)x^3)	\frac{d}{dx}(\frac{5}{12}(3+\sqrt{5})x^{3})
limit as x approaches-infinity of x^0	\lim\:_{x\to\:-\infty\:}(x^{0})
(\partial)/(\partial x)(e^y-xe^x)	\frac{\partial\:}{\partial\:x}(e^{y}-xe^{x})
derivative of (4x^2-3xe^{5x})	\frac{d}{dx}((4x^{2}-3x)e^{5x})
integral of (cos^2(x))^2	\int\:(\cos^{2}(x))^{2}dx
integral of x/(cos^2(x))	\int\:\frac{x}{\cos^{2}(x)}dx
sum from n=0 to infinity of (2n-1)/(n!)	\sum\:_{n=0}^{\infty\:}\frac{2n-1}{n!}
derivative of-x/4	\frac{d}{dx}(-\frac{x}{4})
integral of 1/(sqrt(x^2+x))	\int\:\frac{1}{\sqrt{x^{2}+x}}dx
area y=\|x\|,y=x^2-6	area\:y=\left\|x\right\|,y=x^{2}-6
derivative of 9x^2y^2=1	\frac{d}{dx}9x^{2}y^{2}=1
integral of (tan(x)+sec(x))	\int\:(\tan(x)+\sec(x))dx
(\partial)/(\partial y)((e^x)/(1+e^y))	\frac{\partial\:}{\partial\:y}(\frac{e^{x}}{1+e^{y}})
derivative of f(x)=3	derivative\:f(x)=3
d/(dθ)((csc(θ)+cot(θ))^{-1})	\frac{d}{dθ}((\csc(θ)+\cot(θ))^{-1})
(dy)/(dx)+e^{x+y}=0	\frac{dy}{dx}+e^{x+y}=0
integral of (x^2)/((x^3+5)^2)	\int\:\frac{x^{2}}{(x^{3}+5)^{2}}dx
(\partial)/(\partial x)(sqrt(4x+y^3))	\frac{\partial\:}{\partial\:x}(\sqrt{4x+y^{3}})
limit as x approaches 0 of 1/(sqrt(x))	\lim\:_{x\to\:0}(\frac{1}{\sqrt{x}})
limit as x approaches 1 of sin(pix)	\lim\:_{x\to\:1}(\sin(πx))
(dy)/(dx)= 1/2 y+x	\frac{dy}{dx}=\frac{1}{2}y+x
derivative of f(x)=(10x)/(1-x)	derivative\:f(x)=\frac{10x}{1-x}
taylor cos(x)e^x	taylor\:\cos(x)e^{x}
y^{''}=-a	y^{\prime\:\prime\:}=-a
limit as x approaches-3+of x/(x+3)	\lim\:_{x\to\:-3+}(\frac{x}{x+3})
limit as x approaches 0 of x^3e^{1/x}	\lim\:_{x\to\:0}(x^{3}e^{\frac{1}{x}})

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