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Popular Calculus Problems

integral of (sin^7(4x))/(cos^4(4x))	\int\:\frac{\sin^{7}(4x)}{\cos^{4}(4x)}dx
limit as x approaches 0 of (sin(11x))/x	\lim\:_{x\to\:0}(\frac{\sin(11x)}{x})
derivative of (arcsin(x))^{e^{-x}}	derivative\:(\arcsin(x))^{e^{-x}}
derivative of log_{5}(sin(x))	derivative\:\log_{5}(\sin(x))
integral from 1/5 to 3 of 4xln(5x)	\int\:_{\frac{1}{5}}^{3}4x\ln(5x)dx
sum from n=1 to infinity of 7/(10^n)	\sum\:_{n=1}^{\infty\:}\frac{7}{10^{n}}
tangent of f(x)=2x^3+36x^2+192x+8	tangent\:f(x)=2x^{3}+36x^{2}+192x+8
limit as x approaches 0+of (e^x)/(1-e^{-x)}	\lim\:_{x\to\:0+}(\frac{e^{x}}{1-e^{-x}})
derivative of 4e^{6x}	\frac{d}{dx}(4e^{6x})
derivative of f(x)=sin(3x+1)	derivative\:f(x)=\sin(3x+1)
derivative of (4x^{6x})	\frac{d}{dx}((4x)^{6x})
limit as x approaches pi of xcos((7x)/6)	\lim\:_{x\to\:π}(x\cos(\frac{7x}{6}))
derivative of x/(x+6)	derivative\:\frac{x}{x+6}
integral of-2/(sqrt(7-7x^2))	\int\:-\frac{2}{\sqrt{7-7x^{2}}}dx
derivative of 5x^3-3x^5	\frac{d}{dx}(5x^{3}-3x^{5})
limit as t approaches-2 of (t+4)^2	\lim\:_{t\to\:-2}((t+4)^{2})
limit as x approaches-1 of 5x^2	\lim\:_{x\to\:-1}(5x^{2})
xy+y^'=64x	xy+y^{\prime\:}=64x
tangent of f(x)=x^2+x,\at x=1	tangent\:f(x)=x^{2}+x,\at\:x=1
integral of 7cos(x)-4/(sqrt(1-x^2))	\int\:7\cos(x)-\frac{4}{\sqrt{1-x^{2}}}dx
laplacetransform sin(3t)e^{4t}	laplacetransform\:\sin(3t)e^{4t}
integral of sin(1/2)x	\int\:\sin(\frac{1}{2})xdx
area e^6,e^x,x=0	area\:e^{6},e^{x},x=0
limit as x approaches+2-of (\|x-x\|)/(x-2)	\lim\:_{x\to\:+2-}(\frac{\left\|x-x\right\|}{x-2})
(dy)/(dx)=(3x)/(3+x^2)	\frac{dy}{dx}=\frac{3x}{3+x^{2}}
y^'+x*e^{-x^{2/2}}=0	y^{\prime\:}+x\cdot\:e^{-x^{\frac{2}{2}}}=0
integral of (x-1)cos(x/3)	\int\:(x-1)\cos(\frac{x}{3})dx
derivative of x^{0.2}	\frac{d}{dx}(x^{0.2})
derivative of e^{6sin(7x)}	derivative\:e^{6\sin(7x)}
derivative of pi/3	\frac{d}{dx}(\frac{π}{3})
integral of 1/(sqrt(7+8x^2))	\int\:\frac{1}{\sqrt{7+8x^{2}}}dx
sum from n=0 to infinity of n!(x-4)^n	\sum\:_{n=0}^{\infty\:}n!(x-4)^{n}
derivative of arctan((2x/(1+x^2)))	\frac{d}{dx}(\arctan(\frac{2x}{1+x^{2}}))
d/(dt)(\sqrt[3]{t}+6sqrt(t^3))	\frac{d}{dt}(\sqrt[3]{t}+6\sqrt{t^{3}})
tangent of (x^2)/(x-1)	tangent\:\frac{x^{2}}{x-1}
derivative of f(x)= 1/(ln(x))	derivative\:f(x)=\frac{1}{\ln(x)}
derivative of (3-xe^x/(x+e^x))	\frac{d}{dx}(\frac{3-xe^{x}}{x+e^{x}})
derivative of cos(2xsin(3x))	\frac{d}{dx}(\cos(2x)\sin(3x))
integral of (7x^6-6/(x^6))	\int\:(7x^{6}-\frac{6}{x^{6}})dx
integral of x^2-3x+8	\int\:x^{2}-3x+8dx
slope ofintercept (-7,-6),(10,8)	slopeintercept\:(-7,-6),(10,8)
taylor (3x-10)^{4/3}	taylor\:(3x-10)^{\frac{4}{3}}
(\partial)/(\partial x)(1+x^4+y^4)	\frac{\partial\:}{\partial\:x}(1+x^{4}+y^{4})
y^'=-y^3,y(0)=-2	y^{\prime\:}=-y^{3},y(0)=-2
integral of 3e^{5x}	\int\:3e^{5x}dx
sum from n=1 to infinity of n^2*(0.5)^n	\sum\:_{n=1}^{\infty\:}n^{2}\cdot\:(0.5)^{n}
integral from 1 to infinity of 14e^{-7x}	\int\:_{1}^{\infty\:}14e^{-7x}dx
(dy)/(dx)=-8xy^2	\frac{dy}{dx}=-8xy^{2}
(\partial)/(\partial x)(2x^2y+3xy^2)	\frac{\partial\:}{\partial\:x}(2x^{2}y+3xy^{2})
sum from n=1 to infinity of ((-1)/2)^n	\sum\:_{n=1}^{\infty\:}(\frac{-1}{2})^{n}
(\partial)/(\partial x)((4x+4y)e^y)	\frac{\partial\:}{\partial\:x}((4x+4y)e^{y})
laplacetransform 2e^{-t}cos(2t)	laplacetransform\:2e^{-t}\cos(2t)
sum from n=0 to infinity}((10^{2n of))/(n!)	\sum\:_{n=0}^{\infty\:}\frac{(10^{2n})}{n!}
sum from n=1 to infinity of (n/(n+7))^n	\sum\:_{n=1}^{\infty\:}(\frac{n}{n+7})^{n}
integral from 0 to 1 of x*arcsin(x^2)	\int\:_{0}^{1}x\cdot\:\arcsin(x^{2})dx
integral of (6x^3+3x^2-47x-18)/(x^2-9)	\int\:\frac{6x^{3}+3x^{2}-47x-18}{x^{2}-9}dx
limit as x approaches 1 of (arctan(x)-pi/4)/(x-1)	\lim\:_{x\to\:1}(\frac{\arctan(x)-\frac{π}{4}}{x-1})
integral from-r to r of pi(r^2-x^2)	\int\:_{-r}^{r}π(r^{2}-x^{2})dx
tangent of f(x)=7e^{x^2-5x+8},\at x=0	tangent\:f(x)=7e^{x^{2}-5x+8},\at\:x=0
derivative of (3x^2-6x+6)e^{-8x}	derivative\:(3x^{2}-6x+6)e^{-8x}
y(dy)/(dx)=(y^2-y)(2x+5)	y\frac{dy}{dx}=(y^{2}-y)(2x+5)
derivative of sqrt(a^2-y^2)	derivative\:\sqrt{a^{2}-y^{2}}
(x^2+9)y^'+xy=0	(x^{2}+9)y^{\prime\:}+xy=0
d/(dy)(xcos(y))	\frac{d}{dy}(x\cos(y))
integral of (x^3+x^2)/(x^2+5x+6)	\int\:\frac{x^{3}+x^{2}}{x^{2}+5x+6}dx
derivative of (x^2e^x/(x^2+e^x))	\frac{d}{dx}(\frac{x^{2}e^{x}}{x^{2}+e^{x}})
y^{''}-4y^'+4y^'=0	y^{\prime\:\prime\:}-4y^{\prime\:}+4y^{\prime\:}=0
integral of cos^3(x/(12))	\int\:\cos^{3}(\frac{x}{12})dx
limit as x approaches 4+of (x-4)/(x-4)	\lim\:_{x\to\:4+}(\frac{x-4}{x-4})
tangent of 2x^2-9x+10	tangent\:2x^{2}-9x+10
integral from 0 to 3 of 1	\int\:_{0}^{3}1
(\partial)/(\partial z)(x)	\frac{\partial\:}{\partial\:z}(x)
integral from 0 to 4/3 of 1/(16+9x^2)	\int\:_{0}^{\frac{4}{3}}\frac{1}{16+9x^{2}}dx
integral of sin(9x)cos(4x)	\int\:\sin(9x)\cos(4x)dx
y^{''}+2y^'+6y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+6y=0
y^{''}+25y=20sin(5t)	y^{\prime\:\prime\:}+25y=20\sin(5t)
inverse oflaplace 2s	inverselaplace\:2s
(2x+y)dx-xdy=0	(2x+y)dx-xdy=0
(\partial)/(\partial y)(x+y)	\frac{\partial\:}{\partial\:y}(x+y)
ty^{''}-y^'=0	ty^{\prime\:\prime\:}-y^{\prime\:}=0
(\partial)/(\partial x)((2xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{2xy}{x^{2}+y^{2}})
integral of 3/2 sqrt(t+1)	\int\:\frac{3}{2}\sqrt{t+1}dt
derivative of (5x^2tan(x)/(sec(x)))	\frac{d}{dx}(\frac{5x^{2}\tan(x)}{\sec(x)})
integral from 0 to 1 of (8x^2-5)e^x	\int\:_{0}^{1}(8x^{2}-5)e^{x}dx
(\partial)/(\partial y)(2yt+xj)	\frac{\partial\:}{\partial\:y}(2yt+xj)
integral of (x^2)/(16+x^2)	\int\:\frac{x^{2}}{16+x^{2}}dx
integral of 4t^3y-15t^2-y	\int\:4t^{3}y-15t^{2}-ydt
area 11x-3,10x-5,[12,34]	area\:11x-3,10x-5,[12,34]
integral of 1/(t^2+1)	\int\:\frac{1}{t^{2}+1}dt
limit as x approaches 129 of (x-129)/(sqrt(x+15)-12)	\lim\:_{x\to\:129}(\frac{x-129}{\sqrt{x+15}-12})
derivative of 3^{arctan(x})	\frac{d}{dx}(3^{\arctan(x)})
(\partial)/(\partial x)(xy^2-2y^3+3xz)	\frac{\partial\:}{\partial\:x}(xy^{2}-2y^{3}+3xz)
sum from n=0 to infinity of (n!)/(n^3)	\sum\:_{n=0}^{\infty\:}\frac{n!}{n^{3}}
(\partial)/(\partial x)(3x^2y)	\frac{\partial\:}{\partial\:x}(3x^{2}y)
derivative of sin(x-2)	\frac{d}{dx}(\sin(x-2))
derivative of ((4x-4^5)/((2x-5)^7))	\frac{d}{dx}(\frac{(4x-4)^{5}}{(2x-5)^{7}})
derivative of 38e^{x^2}x	derivative\:38e^{x^{2}}x
integral of 7/(sqrt(5-6x))	\int\:\frac{7}{\sqrt{5-6x}}dx
derivative of 1/2 x^2+2x-2+35x^{-1}	derivative\:\frac{1}{2}x^{2}+2x-2+35x^{-1}
derivative of ln(e^x-e^{-x})	\frac{d}{dx}(\ln(e^{x}-e^{-x}))

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