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Popular Calculus Problems

integral from 1 to 32 of (sin(\sqrt[5]{x}))/(\sqrt[5]{x^4)}	\int\:_{1}^{32}\frac{\sin(\sqrt[5]{x})}{\sqrt[5]{x^{4}}}dx
limit as x approaches 0 of ((1))/(x^2)	\lim\:_{x\to\:0}(\frac{(1)}{x^{2}})
integral of ((x^2-x+12))/(x^3+6x)	\int\:\frac{(x^{2}-x+12)}{x^{3}+6x}dx
(1+cos(x))(dy)/(dx)=(1+e^{-y})sin(x)	(1+\cos(x))\frac{dy}{dx}=(1+e^{-y})\sin(x)
y^'+2xy=e^x	y^{\prime\:}+2xy=e^{x}
integral of x^2+9	\int\:x^{2}+9dx
limit as x approaches-6 of x+1	\lim\:_{x\to\:-6}(x+1)
limit as x approaches-1 of x+x^2+x^3	\lim\:_{x\to\:-1}(x+x^{2}+x^{3})
integral of 1/(y^2sqrt(5-y^2))	\int\:\frac{1}{y^{2}\sqrt{5-y^{2}}}dy
derivative of (xsin(x)/(1+cos(x)))	\frac{d}{dx}(\frac{x\sin(x)}{1+\cos(x)})
integral from 1 to e of 4/z	\int\:_{1}^{e}\frac{4}{z}dz
(\partial)/(\partial y)(x^{1/y})	\frac{\partial\:}{\partial\:y}(x^{\frac{1}{y}})
(d^2)/(dx^2)y+64y=0	\frac{d^{2}}{dx^{2}}y+64y=0
(\partial)/(\partial x)((2y)/(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\frac{2y}{x^{2}-y^{2}})
y^{''}+10y^'+25y=14e^{-5x}	y^{\prime\:\prime\:}+10y^{\prime\:}+25y=14e^{-5x}
limit as x approaches infinity of-1/x	\lim\:_{x\to\:\infty\:}(-\frac{1}{x})
limit as x approaches 1 of cos(pi/3)	\lim\:_{x\to\:1}(\cos(\frac{π}{3}))
derivative of 2/3 pi+1	\frac{d}{dx}(\frac{2}{3}π+1)
(\partial}{\partial x}(\frac{(2x+y))/z)	\frac{\partial\:}{\partial\:x}(\frac{(2x+y)}{z})
integral of cos(4x)cos(5x)	\int\:\cos(4x)\cos(5x)dx
derivative of x^2+6x-3	derivative\:x^{2}+6x-3
49y^{''}+42y^'+9y=0,y(0)=a,y^'(0)=2	49y^{\prime\:\prime\:}+42y^{\prime\:}+9y=0,y(0)=a,y^{\prime\:}(0)=2
area x=((y-3)^2)/3 ,y=9-x	area\:x=\frac{(y-3)^{2}}{3},y=9-x
7sqrt(xy)(dy)/(dx)=2	7\sqrt{xy}\frac{dy}{dx}=2
derivative of 1+5x	\frac{d}{dx}(1+5x)
derivative of (x-2/(x^2+4))	\frac{d}{dx}(\frac{x-2}{x^{2}+4})
12=((33000)dy)/(dt)+1/(22*10^{-6)}y	12=\frac{(33000)dy}{dt}+\frac{1}{22\cdot\:10^{-6}}y
limit as h approaches 0 of 3/(sqrt(3h+1)+1)	\lim\:_{h\to\:0}(\frac{3}{\sqrt{3h+1}+1})
derivative of e^{xi}	\frac{d}{dx}(e^{xi})
(\partial)/(\partial x)(8/(x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\frac{8}{x^{2}+y^{2}+z^{2}})
sum from n=1 to infinity of (4/3)^n	\sum\:_{n=1}^{\infty\:}(\frac{4}{3})^{n}
integral of 3cos^2(x)sin(x)	\int\:3\cos^{2}(x)\sin(x)dx
integral of (2t^2+3)^{4/3}t^3	\int\:(2t^{2}+3)^{\frac{4}{3}}t^{3}dt
derivative of f(x)=(x^2+3x-1)e^x	derivative\:f(x)=(x^{2}+3x-1)e^{x}
derivative of f(x)=-x^2+5x	derivative\:f(x)=-x^{2}+5x
derivative of-3log_{4}(x)	derivative\:-3\log_{4}(x)
limit as n approaches infinity of \|((2n)^{2n})/((2n+2)^{2n)}\|	\lim\:_{n\to\:\infty\:}(\left\|\frac{(2n)^{2n}}{(2n+2)^{2n}}\right\|)
limit as x approaches 2 of 3x-1	\lim\:_{x\to\:2}(3x-1)
(dy)/(dt)=6y+2t-4	\frac{dy}{dt}=6y+2t-4
integral of (-2)/(2x-3)	\int\:\frac{-2}{2x-3}dx
sum from n=1 to infinity of 5^nx^n	\sum\:_{n=1}^{\infty\:}5^{n}x^{n}
derivative of arctan(4x)	derivative\:\arctan(4x)
derivative of e^x+sin(x)	\frac{d}{dx}(e^{x}+\sin(x))
integral of u/(sqrt(u))	\int\:\frac{u}{\sqrt{u}}du
(dy)/(dx)+4y=9	\frac{dy}{dx}+4y=9
derivative of (x-2/(9x^2e^x))	\frac{d}{dx}(\frac{x-2}{9x^{2}e^{x}})
(\partial)/(\partial x)(8ln((3xy)/(5z)))	\frac{\partial\:}{\partial\:x}(8\ln(\frac{3xy}{5z}))
integral of (e^t-\sqrt[4]{16t}+3/(t^3))	\int\:(e^{t}-\sqrt[4]{16t}+\frac{3}{t^{3}})dt
(\partial)/(\partial y)(e^{x+2y}sin(y))	\frac{\partial\:}{\partial\:y}(e^{x+2y}\sin(y))
area g(x)=x^2,[0,1]	area\:g(x)=x^{2},[0,1]
limit as x approaches infinity of 4x-1	\lim\:_{x\to\:\infty\:}(4x-1)
integral from 0 to ln(3) of (e^t)/(sqrt(e^{2t)+49)}	\int\:_{0}^{\ln(3)}\frac{e^{t}}{\sqrt{e^{2t}+49}}dt
(dy)/(dx)=cos^2(y)	\frac{dy}{dx}=\cos^{2}(y)
y^{''}+81y=0	y^{\prime\:\prime\:}+81y=0
inverse oflaplace (60)/(2-5s)	inverselaplace\:\frac{60}{2-5s}
sum from k=1 to infinity of 1/(k^{1+1/k)}	\sum\:_{k=1}^{\infty\:}\frac{1}{k^{1+\frac{1}{k}}}
derivative of f(x)=x^{5/2}	derivative\:f(x)=x^{\frac{5}{2}}
limit as x approaches-1 of x(x+3)	\lim\:_{x\to\:-1}(x(x+3))
sum from n=0 to infinity of (2/7)^n	\sum\:_{n=0}^{\infty\:}(\frac{2}{7})^{n}
area y=sqrt(x+2),y=2,y= 1/(x+1)	area\:y=\sqrt{x+2},y=2,y=\frac{1}{x+1}
y^{''}+256y=64cos(7t)	y^{\prime\:\prime\:}+256y=64\cos(7t)
integral from 0 to pi of sin^2(t)	\int\:_{0}^{π}\sin^{2}(t)dt
derivative of 4/(x-2)	\frac{d}{dx}(\frac{4}{x-2})
derivative of ln(3+2x)	\frac{d}{dx}(\ln(3+2x))
limit as x approaches 1 of sqrt(x^2+1)	\lim\:_{x\to\:1}(\sqrt{x^{2}+1})
integral of 1+x	\int\:1+xdx
derivative of (3x+5)^4sqrt(x)	derivative\:(3x+5)^{4}\sqrt{x}
integral of te^{-2}	\int\:te^{-2}dt
derivative of y=-4x^7-1	derivative\:y=-4x^{7}-1
integral of (cos(x)-sin(x))	\int\:(\cos(x)-\sin(x))dx
derivative of 1-1/(sqrt(1-x^2))	\frac{d}{dx}(1-\frac{1}{\sqrt{1-x^{2}}})
(\partial)/(\partial x)((9x^2)/((x-y)^2))	\frac{\partial\:}{\partial\:x}(\frac{9x^{2}}{(x-y)^{2}})
integral from 0 to 1 of (x)	\int\:_{0}^{1}(x)dx
integral of-(3(x+a))/(x^2+a^2)	\int\:-\frac{3(x+a)}{x^{2}+a^{2}}dx
integral of cot^6(2x)	\int\:\cot^{6}(2x)dx
implicit (dy)/(dx),y=(arctan(9x))^2	implicit\:\frac{dy}{dx},y=(\arctan(9x))^{2}
integral from 0 to infinity of 1/(x^2+9)	\int\:_{0}^{\infty\:}\frac{1}{x^{2}+9}dx
limit as x approaches-5 of 1/(x^2-25)	\lim\:_{x\to\:-5}(\frac{1}{x^{2}-25})
integral of (x-1)/x	\int\:\frac{x-1}{x}dx
tangent of f(x)=ln(x^3),\at x=e^5	tangent\:f(x)=\ln(x^{3}),\at\:x=e^{5}
tangent of f(x)=(x^3+6x)^4,\at x=2	tangent\:f(x)=(x^{3}+6x)^{4},\at\:x=2
integral from 0 to 2 of (2x)/((x^2+3)^3)	\int\:_{0}^{2}\frac{2x}{(x^{2}+3)^{3}}dx
slope of x^2+x	slope\:x^{2}+x
derivative of sin((pix)/3)	derivative\:\sin(\frac{πx}{3})
integral of ((4+x+x^2))/(sqrt(x))	\int\:\frac{(4+x+x^{2})}{\sqrt{x}}dx
derivative of f(x)=ln((x^2-1)/(x^2+1))	derivative\:f(x)=\ln(\frac{x^{2}-1}{x^{2}+1})
derivative of (3+x^2/(3-x))	\frac{d}{dx}(\frac{3+x^{2}}{3-x})
implicit x^3y^3-y=x	implicit\:x^{3}y^{3}-y=x
derivative of sin(x+cos(y))	\frac{d}{dx}(\sin(x)+\cos(y))
derivative of f(x)= 3/(2x-4)	derivative\:f(x)=\frac{3}{2x-4}
(\partial)/(\partial x)(xe^{4y}sin(3z))	\frac{\partial\:}{\partial\:x}(xe^{4y}\sin(3z))
integral of 2/(x^2+10x+29)	\int\:\frac{2}{x^{2}+10x+29}dx
(1+x^2)(dy)/(dx)-(1+y^2)=0	(1+x^{2})\frac{dy}{dx}-(1+y^{2})=0
tangent of f(x)=sqrt(x^2-x+5),\at x=5	tangent\:f(x)=\sqrt{x^{2}-x+5},\at\:x=5
derivative of 1/(sqrt(1+sin^2(x)))	\frac{d}{dx}(\frac{1}{\sqrt{1+\sin^{2}(x)}})
derivative of 2e^{-x^2}x-2e^{-x^2}x^3	\frac{d}{dx}(2e^{-x^{2}}x-2e^{-x^{2}}x^{3})
derivative of f(x)=2x^{-3/4}	derivative\:f(x)=2x^{-\frac{3}{4}}
derivative of 3x-5x^2	derivative\:3x-5x^{2}
d/(d{x)}(e^{(3{x}^2{y}+4{z})}-{x}{y}^3{z}^4+({x}^2)/(2{y)}-4{x}^3{z}^4)	\frac{d}{d{x}}(e^{(3{x}^{2}{y}+4{z})}-{x}{y}^{3}{z}^{4}+\frac{{x}^{2}}{2{y}}-4{x}^{3}{z}^{4})
integral of e^{-st}(1)	\int\:e^{-st}(1)dt

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