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Popular Calculus Problems

sum from n=0 to infinity of n/(n^3+1)	\sum\:_{n=0}^{\infty\:}\frac{n}{n^{3}+1}
integral of 8sin^5(x)	\int\:8\sin^{5}(x)dx
integral of ln(5^u)	\int\:\ln(5^{u})du
derivative of cos(nx)	\frac{d}{dx}(\cos(nx))
(dy)/(dx)=x^3y^3	\frac{dy}{dx}=x^{3}y^{3}
(\partial)/(\partial x)(xarcsin(y/x))	\frac{\partial\:}{\partial\:x}(x\arcsin(\frac{y}{x}))
derivative of (x^2+9)^2(x-9)	derivative\:(x^{2}+9)^{2}(x-9)
(d^5)/(dx^5)(x^{11/2})	\frac{d^{5}}{dx^{5}}(x^{\frac{11}{2}})
integral of sqrt(x)+1	\int\:\sqrt{x}+1dx
limit as x approaches 0 of 4/(x^3(x+3))	\lim\:_{x\to\:0}(\frac{4}{x^{3}(x+3)})
taylor sin(x),1	taylor\:\sin(x),1
derivative of (x^2)/(28)	derivative\:\frac{x^{2}}{28}
derivative of cos(2x+sin(2x))	\frac{d}{dx}(\cos(2x)+\sin(2x))
derivative of x^2+x+3	derivative\:x^{2}+x+3
(tdu)/(dt)=t^2+3u,\H(4)=48	\frac{tdu}{dt}=t^{2}+3u,\H(4)=48
(\partial)/(\partial x)(x^2+ycos(xy))	\frac{\partial\:}{\partial\:x}(x^{2}+y\cos(xy))
integral of 4sec^4(x)tan(x)	\int\:4\sec^{4}(x)\tan(x)dx
derivative of (x^5/5+1/(12x^3))	\frac{d}{dx}(\frac{x^{5}}{5}+\frac{1}{12x^{3}})
tangent of y=(x+2)/(x-2),(3,5)	tangent\:y=\frac{x+2}{x-2},(3,5)
integral of (8x^3+3)/((x^2+2)^2)	\int\:\frac{8x^{3}+3}{(x^{2}+2)^{2}}dx
(\partial)/(\partial x)(sin^2(mx+ny))	\frac{\partial\:}{\partial\:x}(\sin^{2}(mx+ny))
integral of 2^{sin^2(1/3 x)}sin(2/3 x)	\int\:2^{\sin^{2}(\frac{1}{3}x)}\sin(\frac{2}{3}x)dx
taylor 1/(x^2),-1	taylor\:\frac{1}{x^{2}},-1
derivative of 7/(sqrt(x^4+3))	\frac{d}{dx}(\frac{7}{\sqrt{x^{4}+3}})
limit as x approaches pi/4 of (tan(x))^{tan(2x)}	\lim\:_{x\to\:\frac{π}{4}}((\tan(x))^{\tan(2x)})
limit as x approaches 5+of ln(x^2-25)	\lim\:_{x\to\:5+}(\ln(x^{2}-25))
derivative of y=xsqrt(16-x^2)	derivative\:y=x\sqrt{16-x^{2}}
derivative of ln(cos^2(x))	\frac{d}{dx}(\ln(\cos^{2}(x)))
integral from 0 to pi/8 of cos(4x)	\int\:_{0}^{\frac{π}{8}}\cos(4x)dx
(\partial)/(\partial x)({f}(x)(x{f}(x)(x{f}(x))))	\frac{\partial\:}{\partial\:x}({f}(x)(x{f}(x)(x{f}(x))))
integral of e^{2x}arcsin(e^x)	\int\:e^{2x}\arcsin(e^{x})dx
derivative of (x^3+x)^6	derivative\:(x^{3}+x)^{6}
(\partial)/(\partial y)(1-x^2y)	\frac{\partial\:}{\partial\:y}(1-x^{2}y)
integral of x/((1+x))	\int\:\frac{x}{(1+x)}dx
derivative of (4x-7^2)	\frac{d}{dx}((4x-7)^{2})
derivative of (cos(x)dx)	\frac{d}{dx}((\cos(x))dx)
taylor ln(x+3)	taylor\:\ln(x+3)
(\partial)/(\partial y)(-x/(x^2+y^2))	\frac{\partial\:}{\partial\:y}(-\frac{x}{x^{2}+y^{2}})
derivative of sin^3(cos(x))	\frac{d}{dx}(\sin^{3}(\cos(x)))
(d^2y}{dx^2}=\frac{(6x^5))/5-3x	\frac{d^{2}y}{dx^{2}}=\frac{(6x^{5})}{5}-3x
derivative of y=(x^2+1)/(x+1)	derivative\:y=\frac{x^{2}+1}{x+1}
(\partial}{\partial x}(\frac{2y)/x)	\frac{\partial\:}{\partial\:x}(\frac{2y}{x})
limit as x approaches 0 of 4/(3+e^{1/x)}	\lim\:_{x\to\:0}(\frac{4}{3+e^{\frac{1}{x}}})
derivative of sin(2x+3y)	\frac{d}{dx}(\sin(2x+3y))
(\partial)/(\partial y)(ln(x^2+y))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y))
area x^4-2x^2,2x^2,[0,2]	area\:x^{4}-2x^{2},2x^{2},[0,2]
tangent of f(x)=(8x)/(x+7),(2,1.7777700000000…)	tangent\:f(x)=\frac{8x}{x+7},(2,1.7777700000000…)
tangent of y=5^{x-3},(3,1)	tangent\:y=5^{x-3},(3,1)
derivative of f(x)=x^3-2x^2+x+1	derivative\:f(x)=x^{3}-2x^{2}+x+1
integral from-2 to-1 of 1/((x-1)^3)	\int\:_{-2}^{-1}\frac{1}{(x-1)^{3}}dx
area 7x+12,0,10	area\:7x+12,0,10
inverse oflaplace 1/(s^3(s+2))	inverselaplace\:\frac{1}{s^{3}(s+2)}
(\partial)/(\partial x)(x^2y+y^2z+z^2x)	\frac{\partial\:}{\partial\:x}(x^{2}y+y^{2}z+z^{2}x)
x^{-2}y^{-5}dx+x^{-3}y^{-4}dy=0	x^{-2}y^{-5}dx+x^{-3}y^{-4}dy=0
integral of (x^2)/(sqrt(1+x^3))	\int\:\frac{x^{2}}{\sqrt{1+x^{3}}}dx
integral of 18cos(3x)	\int\:18\cos(3x)dx
integral from 0 to 1 of x^2-x^4	\int\:_{0}^{1}x^{2}-x^{4}dx
integral from e to 3 of 1/(16-x^2)	\int\:_{e}^{3}\frac{1}{16-x^{2}}dx
integral from 0 to pi of 1+sin(x)	\int\:_{0}^{π}1+\sin(x)dx
(dy)/(dt)=t*sqrt(y)	\frac{dy}{dt}=t\cdot\:\sqrt{y}
integral from 0 to 1 of ln(1+x)	\int\:_{0}^{1}\ln(1+x)dx
integral of (-2^{3-2x})	\int\:(-2^{3-2x})dx
(\partial)/(\partial y)(cos(x)+sin(y))	\frac{\partial\:}{\partial\:y}(\cos(x)+\sin(y))
f(x)=\sqrt[3]{6x+8}	f(x)=\sqrt[3]{6x+8}
derivative of tan^2(sin(x))	\frac{d}{dx}(\tan^{2}(\sin(x)))
derivative of f(x)=sqrt(x+7)	derivative\:f(x)=\sqrt{x+7}
area x=((y-2)^2)/3 ,y=8-x	area\:x=\frac{(y-2)^{2}}{3},y=8-x
derivative of (x^2+2^{-5}cos(x))	\frac{d}{dx}((x^{2}+2)^{-5}\cos(x))
area y=x^2,(0,2)	area\:y=x^{2},(0,2)
integral of cos(x)x^2	\int\:\cos(x)x^{2}dx
integral of (2x^3+1)^2	\int\:(2x^{3}+1)^{2}dx
derivative of sqrt(x+\sqrt{1+cos(x^2)})	\frac{d}{dx}(\sqrt{x+\sqrt{1+\cos(x^{2})}})
integral of t^2sec^2(t)	\int\:t^{2}\sec^{2}(t)dt
integral of (1-xy)^{-2}	\int\:(1-xy)^{-2}dx
integral of (e^{-3x})	\int\:(e^{-3x})dx
limit as x approaches 3 of (x^3-8)/(x-2)	\lim\:_{x\to\:3}(\frac{x^{3}-8}{x-2})
sum from n=0 to infinity of e^{-0.02n}	\sum\:_{n=0}^{\infty\:}e^{-0.02n}
laplacetransform (t+7)^3	laplacetransform\:(t+7)^{3}
derivative of (t-sqrt(t))/(t^{1/6)}	derivative\:\frac{t-\sqrt{t}}{t^{\frac{1}{6}}}
tangent of (2x-1)^2	tangent\:(2x-1)^{2}
integral of (16)/((x^2-4)(x-2))	\int\:\frac{16}{(x^{2}-4)(x-2)}dx
((((dy)/(dx))-e^{-x}+5))/y =-5	\frac{((\frac{dy}{dx})-e^{-x}+5)}{y}=-5
derivative of x^{0.3}	\frac{d}{dx}(x^{0.3})
integral of 2cos^2(3x)	\int\:2\cos^{2}(3x)dx
limit as x approaches infinity of 9/2	\lim\:_{x\to\:\infty\:}(\frac{9}{2})
derivative of y=8^{4^{x^2}}	derivative\:y=8^{4^{x^{2}}}
integral of (-9x^2)/((3-3x^3)^2)	\int\:\frac{-9x^{2}}{(3-3x^{3})^{2}}dx
taylor x^{3/2},4	taylor\:x^{\frac{3}{2}},4
(\partial)/(\partial x)(-210(5x-y)^5)	\frac{\partial\:}{\partial\:x}(-210(5x-y)^{5})
derivative of 1+csqrt(1-x^2)	\frac{d}{dx}(1+c\sqrt{1-x^{2}})
slope of y=(6x)/(x^2+1)	slope\:y=\frac{6x}{x^{2}+1}
integral from-2 to 2 of 1	\int\:_{-2}^{2}1dx
derivative of tan(x^8)	derivative\:\tan(x^{8})
tangent of y=(1+5x)^{11},(0,1)	tangent\:y=(1+5x)^{11},(0,1)
integral of (x^3)/((x^2+5)^2)	\int\:\frac{x^{3}}{(x^{2}+5)^{2}}dx
derivative of 120x^3-240x^2+120x	\frac{d}{dx}(120x^{3}-240x^{2}+120x)
integral of cos(x)+1/5 x	\int\:\cos(x)+\frac{1}{5}xdx
integral from 2 to 5 of 8x^7	\int\:_{2}^{5}8x^{7}dx
area y=-1/5 x^2-6/5 x+7/5 ,(-5,5)	area\:y=-\frac{1}{5}x^{2}-\frac{6}{5}x+\frac{7}{5},(-5,5)
integral of e^x*sin(2x)	\int\:e^{x}\cdot\:\sin(2x)dx

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