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Popular Calculus Problems

integral of x(x-4)^5	\int\:x(x-4)^{5}dx
limit as n approaches infinity of 3^n	\lim\:_{n\to\:\infty\:}(3^{n})
derivative of (x+2^3(2x-1)^5)	\frac{d}{dx}((x+2)^{3}(2x-1)^{5})
integral from 0 to pi/4 of sin(4x)	\int\:_{0}^{\frac{π}{4}}\sin(4x)dx
integral from 0 to x of (sin^2(t))	\int\:_{0}^{x}(\sin^{2}(t))dt
(dy)/(dx)=-0.13*(100-y)	\frac{dy}{dx}=-0.13\cdot\:(100-y)
sum from n=0 to infinity of n/((n+1))	\sum\:_{n=0}^{\infty\:}\frac{n}{(n+1)}
integral of 3xy+2	\int\:3xy+2dy
slope of (-1,2),(4,0)	slope\:(-1,2),(4,0)
integral of (6x+2)^{-1}	\int\:(6x+2)^{-1}dx
derivative of f(x)=x^{4.5}	derivative\:f(x)=x^{4.5}
xy^'+3y=4x	xy^{\prime\:}+3y=4x
limit as x approaches+1 of 2x^3-3x^2+x+2	\lim\:_{x\to\:+1}(2x^{3}-3x^{2}+x+2)
(dy)/(dx)=3x^2	\frac{dy}{dx}=3x^{2}
derivative of y=ln(5)x^2	derivative\:y=\ln(5)x^{2}
integral of-2xe^x	\int\:-2xe^{x}dx
limit as x approaches 0-of x/(15x^5-5x)	\lim\:_{x\to\:0-}(\frac{x}{15x^{5}-5x})
integral of 4/((9-2x)^3)	\int\:\frac{4}{(9-2x)^{3}}dx
maclaurin f(x)=(2x-1)^2	maclaurin\:f(x)=(2x-1)^{2}
integral from 0 to pi/4 of x^3cos(x)	\int\:_{0}^{\frac{π}{4}}x^{3}\cos(x)dx
integral of sqrt(x)cos(sqrt(x^3))	\int\:\sqrt{x}\cos(\sqrt{x^{3}})dx
integral from 0 to 1 of e^{6x}	\int\:_{0}^{1}e^{6x}dx
integral of (3y^3-2y^2+(e^y)/6)	\int\:(3y^{3}-2y^{2}+\frac{e^{y}}{6})dy
derivative of (-2sqrt(x)/(-4x^4))	\frac{d}{dx}(\frac{-2\sqrt{x}}{-4x^{4}})
integral from 0 to 2 of 1/(sqrt(x^2+4))	\int\:_{0}^{2}\frac{1}{\sqrt{x^{2}+4}}dx
(\partial)/(\partial x)(x^4y^3+8x^2y)	\frac{\partial\:}{\partial\:x}(x^{4}y^{3}+8x^{2}y)
derivative of (x-5/5)	\frac{d}{dx}(\frac{x-5}{5})
derivative of sqrt(81-y^2)	derivative\:\sqrt{81-y^{2}}
y^'=6-3y	y^{\prime\:}=6-3y
limit as x approaches 0 of (tan(12x))/x	\lim\:_{x\to\:0}(\frac{\tan(12x)}{x})
limit as x approaches infinity of 3x+7	\lim\:_{x\to\:\infty\:}(3x+7)
tangent of-(6x)/(x^2+1)	tangent\:-\frac{6x}{x^{2}+1}
limit as w approaches-2 of (w^2+5w+6)/(w^3+8)	\lim\:_{w\to\:-2}(\frac{w^{2}+5w+6}{w^{3}+8})
((e^{2x}))/(x^2+1)	\frac{(e^{2x})}{x^{2}+1}
derivative of x^2-x+3	\frac{d}{dx}(x^{2}-x+3)
(\partial)/(\partial x)(x^{3/4})	\frac{\partial\:}{\partial\:x}(x^{\frac{3}{4}})
derivative of e^x-x	derivative\:e^{x}-x
taylor 2x	taylor\:2x
y'=(y-1)^2x^3	y\prime\:=(y-1)^{2}x^{3}
derivative of e^x(9-5x+5x^2)	derivative\:e^{x}(9-5x+5x^{2})
derivative of cos(-x/3)	\frac{d}{dx}(\cos(-\frac{x}{3}))
laplacetransform t^2sin(3t)	laplacetransform\:t^{2}\sin(3t)
integral from-3 to 3 of 12-x^2-(x^2-6)	\int\:_{-3}^{3}12-x^{2}-(x^{2}-6)dx
limit as x approaches 2 of 9+(-12)	\lim\:_{x\to\:2}(9+(-12))
derivative of 1/(1+4x^2)	\frac{d}{dx}(\frac{1}{1+4x^{2}})
limit as x approaches 0 of (x^2)/(sin^2(7x))	\lim\:_{x\to\:0}(\frac{x^{2}}{\sin^{2}(7x)})
f(x)=4sec(x)	f(x)=4\sec(x)
(\partial)/(\partial x)(3sqrt(xy^2-2xy+z))	\frac{\partial\:}{\partial\:x}(3\sqrt{xy^{2}-2xy+z})
y^{''}-4y^'+7y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+7y=0
integral from-2 to 3 of (28)/(x^4)	\int\:_{-2}^{3}\frac{28}{x^{4}}dx
tangent of x^2=y^2,(1,-1)	tangent\:x^{2}=y^{2},(1,-1)
tangent of f(x)=x^2-7x+7,\at x=0	tangent\:f(x)=x^{2}-7x+7,\at\:x=0
(\partial)/(\partial x)(-y*cos(x))	\frac{\partial\:}{\partial\:x}(-y\cdot\:\cos(x))
xy^'=(1-4x^2)tan(y)	xy^{\prime\:}=(1-4x^{2})\tan(y)
integral of (2e^x)/(e^{2x)+10e^x+25}	\int\:\frac{2e^{x}}{e^{2x}+10e^{x}+25}dx
integral of (x^3)/((x-1)^4)	\int\:\frac{x^{3}}{(x-1)^{4}}dx
integral from 2 to infinity of ye^{-9y}	\int\:_{2}^{\infty\:}ye^{-9y}dy
(d^2)/(dx^2)((x^3+2x)^6)	\frac{d^{2}}{dx^{2}}((x^{3}+2x)^{6})
sum from n=0 to infinity of (x/(n!))^n	\sum\:_{n=0}^{\infty\:}(\frac{x}{n!})^{n}
derivative of y=(x+4)^5(x+1)^2	derivative\:y=(x+4)^{5}(x+1)^{2}
integral of (3x^2-2)/((x+2)^3)	\int\:\frac{3x^{2}-2}{(x+2)^{3}}dx
integral from 1 to x of f(t)	\int\:_{1}^{x}f(t)dt
xy(dx-dy)=x^2dy+y^2dx	xy(dx-dy)=x^{2}dy+y^{2}dx
y^{''}+8y^'+17y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+17y=0
derivative of (x^3+1(x^2-3x))	\frac{d}{dx}((x^{3}+1)(x^{2}-3x))
(d^2)/(dx^2)(x^2-1/(x^2))	\frac{d^{2}}{dx^{2}}(x^{2}-\frac{1}{x^{2}})
integral from 0 to 4 of 2^x	\int\:_{0}^{4}2^{x}dx
derivative of 2x^3+3	\frac{d}{dx}(2x^{3}+3)
integral of sqrt(e^t)	\int\:\sqrt{e^{t}}dt
y^{''}+2y^'+y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(0)=0,y^{\prime\:}(0)=1
xy^'+y=xe^x	xy^{\prime\:}+y=xe^{x}
derivative of c_{1}e^{-x}+c_{2}xe^{-x}	\frac{d}{dx}(c_{1}e^{-x}+c_{2}xe^{-x})
integral of cot(x	\int\:\cot(d)xdx
integral of 5^u	\int\:5^{u}du
integral of ln(x^2+2)	\int\:\ln(x^{2}+2)dx
integral of 17sin^2(xco)s^2x	\int\:17\sin^{2}(xco)s^{2}xdx
integral of sin^2(3t)	\int\:\sin^{2}(3t)dt
tangent of f(x)=\sqrt[4]{x}-x,\at x=1	tangent\:f(x)=\sqrt[4]{x}-x,\at\:x=1
integral of 5sin(ln(x))	\int\:5\sin(\ln(x))dx
f(x)= x/(x^2+36)	f(x)=\frac{x}{x^{2}+36}
integral of x^2(5-x)^4	\int\:x^{2}(5-x)^{4}dx
derivative of 2ln(x+1)	derivative\:2\ln(x+1)
sum from n=1 to infinity of (n!)/(107^n)	\sum\:_{n=1}^{\infty\:}\frac{n!}{107^{n}}
derivative of x^3+xy^2e^{x/y}	\frac{d}{dx}(x^{3}+xy^{2}e^{\frac{x}{y}})
-y^{''}-y+x^2=0	-y^{\prime\:\prime\:}-y+x^{2}=0
limit as x approaches infinity of (3x)/2	\lim\:_{x\to\:\infty\:}(\frac{3x}{2})
integral of (x^2-x+18)/(x^3+3x)	\int\:\frac{x^{2}-x+18}{x^{3}+3x}dx
integral of 1/(10x-x^2)	\int\:\frac{1}{10x-x^{2}}dx
derivative of 0.2e^{5x}	\frac{d}{dx}(0.2e^{5x})
derivative of f(x)=sin^5(3x^2-x+13)	derivative\:f(x)=\sin^{5}(3x^{2}-x+13)
derivative of (81)/((6(1/6)+8)^{5/2)}	derivative\:\frac{81}{(6(\frac{1}{6})+8)^{\frac{5}{2}}}
derivative of (arctan(5x))^2	derivative\:(\arctan(5x))^{2}
derivative of sqrt(x-2)+sqrt(y-1)	\frac{d}{dx}(\sqrt{x-2}+\sqrt{y-1})
limit as x approaches 1+of (x+10)/(1-x)	\lim\:_{x\to\:1+}(\frac{x+10}{1-x})
tangent of x^2+xy+y^2=3,(1,1)	tangent\:x^{2}+xy+y^{2}=3,(1,1)
limit as x approaches 7 of ((x^2-5x-14))/(x-7)	\lim\:_{x\to\:7}(\frac{(x^{2}-5x-14)}{x-7})
y^'+1/(200+t)y=0,y(0)=60	y^{\prime\:}+\frac{1}{200+t}y=0,y(0)=60
integral of (4x^2sin(2x))/9	\int\:\frac{4x^{2}\sin(2x)}{9}dx
sum from n=2 to infinity of (n-2)/(n5^n)	\sum\:_{n=2}^{\infty\:}\frac{n-2}{n5^{n}}
sum from n=3 to infinity of (7^n)/(14^n)	\sum\:_{n=3}^{\infty\:}\frac{7^{n}}{14^{n}}

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