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Popular Calculus Problems

limit as x approaches 1 of-6	\lim\:_{x\to\:1}(-6)
limit as x approaches-pi of cos(x+pi)-1	\lim\:_{x\to\:-π}(\cos(x+π)-1)
integral of 1/((4x^2-25)^2)	\int\:\frac{1}{(4x^{2}-25)^{2}}dx
area x-1,sqrt(2x+6),[-2,4]	area\:x-1,\sqrt{2x+6},[-2,4]
derivative of (2x/((x^2-3)^3))	\frac{d}{dx}(\frac{2x}{(x^{2}-3)^{3}})
3y^{''}-16y^'+5y=0,y(0)=-3,y^'(0)=4	3y^{\prime\:\prime\:}-16y^{\prime\:}+5y=0,y(0)=-3,y^{\prime\:}(0)=4
derivative of 1/((x-4)^2)	derivative\:\frac{1}{(x-4)^{2}}
derivative of f(x)=(3x^2+6x)^3	derivative\:f(x)=(3x^{2}+6x)^{3}
integral of 0.06x^2-4.4x+60	\int\:0.06x^{2}-4.4x+60dx
limit as x approaches 0 of 2xtan(3x)	\lim\:_{x\to\:0}(2x\tan(3x))
tangent of f(x)=x^3-2x^2-3x	tangent\:f(x)=x^{3}-2x^{2}-3x
integral from 1 to 8 of 1	\int\:_{1}^{8}1dx
integral from 0 to 1 of 7xe^{x^2}	\int\:_{0}^{1}7xe^{x^{2}}dx
y^{''}-6y^'+4y=0,y(0)=0,y^'(0)=1	y^{\prime\:\prime\:}-6y^{\prime\:}+4y=0,y(0)=0,y^{\prime\:}(0)=1
derivative of 2(3-x^2)^7	derivative\:2(3-x^{2})^{7}
derivative of sqrt(cos(2x))	\frac{d}{dx}(\sqrt{\cos(2x)})
integral of x/(sqrt(3-4x^2))	\int\:\frac{x}{\sqrt{3-4x^{2}}}dx
limit as x approaches infinity of 91	\lim\:_{x\to\:\infty\:}(91)
integral of (2x)/(x^2+sqrt(2)x+1)	\int\:\frac{2x}{x^{2}+\sqrt{2}x+1}dx
integral of (12x+5)	\int\:(12x+5)dx
(x^2+1)(dy)/(dx)+8x(y-1)=0	(x^{2}+1)\frac{dy}{dx}+8x(y-1)=0
integral of (40x^2)/(x^4-52x^2+576)	\int\:\frac{40x^{2}}{x^{4}-52x^{2}+576}dx
slope of (2,3),(-2,-3)	slope\:(2,3),(-2,-3)
derivative of 4/(2x+1)	\frac{d}{dx}(\frac{4}{2x+1})
tangent of f(x)=2x^2+x-1,\at x=0	tangent\:f(x)=2x^{2}+x-1,\at\:x=0
derivative of log_{10}(x/(sqrt(x^2+1)))	\frac{d}{dx}(\log_{10}(\frac{x}{\sqrt{x^{2}+1}}))
(\partial)/(\partial x)(sqrt(15-2x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{15-2x^{2}-y^{2}})
derivative of (3+x^4)^{4/5}	derivative\:(3+x^{4})^{\frac{4}{5}}
limit as x approaches 0+of (10)/(x^2)	\lim\:_{x\to\:0+}(\frac{10}{x^{2}})
derivative of f(x)=17e^x-ex^e	derivative\:f(x)=17e^{x}-ex^{e}
derivative of f(x)= x/(x+2)	derivative\:f(x)=\frac{x}{x+2}
(dy)/(dt)=9t^2	\frac{dy}{dt}=9t^{2}
limit as x approaches-2 of 3x^2-3x-8	\lim\:_{x\to\:-2}(3x^{2}-3x-8)
tangent of f(x)=6x-x^2,\at x=-1	tangent\:f(x)=6x-x^{2},\at\:x=-1
f^'(θ)=cos(θ)-sin(θ)	f^{\prime\:}(θ)=\cos(θ)-\sin(θ)
(\partial)/(\partial y)(4x^3y^3+4)	\frac{\partial\:}{\partial\:y}(4x^{3}y^{3}+4)
integral from-1 to 3 of \|4-x^2\|	\int\:_{-1}^{3}\left\|4-x^{2}\right\|dx
area y= 3/x ,y=7x,y= 1/7 x	area\:y=\frac{3}{x},y=7x,y=\frac{1}{7}x
derivative of f(x)=((x^2-6x))/(x+1)	derivative\:f(x)=\frac{(x^{2}-6x)}{x+1}
derivative of e^{x/a}	\frac{d}{dx}(e^{\frac{x}{a}})
integral of xe^{-1/2 x}	\int\:xe^{-\frac{1}{2}x}dx
limit as x approaches 2 of 10^{x^2-4x}	\lim\:_{x\to\:2}(10^{x^{2}-4x})
integral of ex^{e+1}	\int\:ex^{e+1}dx
f(x)=2xsqrt(1-x^2)	f(x)=2x\sqrt{1-x^{2}}
derivative of f(x)=(8x^2-13x)e^x	derivative\:f(x)=(8x^{2}-13x)e^{x}
integral from 0 to 5 of sqrt(25+x^2)	\int\:_{0}^{5}\sqrt{25+x^{2}}dx
integral of (sec^2(x))/(1+tan(x))	\int\:\frac{\sec^{2}(x)}{1+\tan(x)}dx
sum from n=1 to infinity of (3n)/(4n+1)	\sum\:_{n=1}^{\infty\:}\frac{3n}{4n+1}
((x+2)^{(2)}(dy))/((dx))=5-8y-4xy	\frac{(x+2)^{(2)}(dy)}{(dx)}=5-8y-4xy
integral of ((y-2))/(y+3)	\int\:\frac{(y-2)}{y+3}dy
integral from 0 to 0.6 of 2xe^{-x}	\int\:_{0}^{0.6}2xe^{-x}dx
y^'=2y	y^{\prime\:}=2y
(dy)/(dx)=y^{1/3}	\frac{dy}{dx}=y^{\frac{1}{3}}
tangent of sqrt(x^2+11),\at x=5	tangent\:\sqrt{x^{2}+11},\at\:x=5
derivative of t^{sqrt(13t)}	derivative\:t^{\sqrt{13t}}
derivative of sec(5x+1)	\frac{d}{dx}(\sec(5x)+1)
derivative of f(x)=4x^{5/4}+4x^{3/2}+8x	derivative\:f(x)=4x^{\frac{5}{4}}+4x^{\frac{3}{2}}+8x
(x-1)^3(dy)/(dx)+4(x-1)^2y=x+1	(x-1)^{3}\frac{dy}{dx}+4(x-1)^{2}y=x+1
y^'=-(1+x+y)/(1+x)	y^{\prime\:}=-\frac{1+x+y}{1+x}
integral of (cos(6x))/(1+sin^2(6x))	\int\:\frac{\cos(6x)}{1+\sin^{2}(6x)}dx
integral of 1/(9-5x)	\int\:\frac{1}{9-5x}dx
(x+ye^{y/x})dx-xe^{y/x}dy=0,y(0)=4	(x+ye^{\frac{y}{x}})dx-xe^{\frac{y}{x}}dy=0,y(0)=4
integral of sqrt(5x+7)	\int\:\sqrt{5x+7}dx
integral of 2x^2y	\int\:2x^{2}ydy
integral of-picsc((pix)/2)cot((pix)/2)	\int\:-π\csc(\frac{πx}{2})\cot(\frac{πx}{2})dx
derivative of (x^2/(3x-1))	\frac{d}{dx}(\frac{x^{2}}{3x-1})
(\partial)/(\partial x)(8^x)	\frac{\partial\:}{\partial\:x}(8^{x})
integral from 1 to sqrt(x of) 1/(1+t^2)	\int\:_{1}^{\sqrt{x}}\frac{1}{1+t^{2}}dt
derivative of e^x(3x^2-5x)	derivative\:e^{x}(3x^{2}-5x)
(dy)/(dx)=((-y^2))/((1+y^2))*(e^{-x})	\frac{dy}{dx}=\frac{(-y^{2})}{(1+y^{2})}\cdot\:(e^{-x})
derivative of-2sin(x-xcos(x))	\frac{d}{dx}(-2\sin(x)-x\cos(x))
integral of (e^{3sqrt(x)})/(sqrt(x))	\int\:\frac{e^{3\sqrt{x}}}{\sqrt{x}}dx
tangent of f(x)=(sqrt(x))/(x+1)	tangent\:f(x)=\frac{\sqrt{x}}{x+1}
limit as x approaches-2 of 1/((x+2)^5)	\lim\:_{x\to\:-2}(\frac{1}{(x+2)^{5}})
inverse oflaplace 1/(s(s^2+2s+3))	inverselaplace\:\frac{1}{s(s^{2}+2s+3)}
integral of (2x+3)/(x^2+9)	\int\:\frac{2x+3}{x^{2}+9}dx
derivative of y=ln(cos(x))	derivative\:y=\ln(\cos(x))
derivative of (ln(x^2-3)^3)	\frac{d}{dx}((\ln(x^{2}-3))^{3})
implicit (dy)/(dx),x^2+y^2=4	implicit\:\frac{dy}{dx},x^{2}+y^{2}=4
derivative of y=log_{3}(8x-1)	derivative\:y=\log_{3}(8x-1)
(d^2)/(dx^2)(sqrt(1+x^2))	\frac{d^{2}}{dx^{2}}(\sqrt{1+x^{2}})
y^'+y/(6960)=0.0025862069	y^{\prime\:}+\frac{y}{6960}=0.0025862069
derivative of e^{(-x})	\frac{d}{dx}(e^{(-x)})
integral of 3x	\int\:3xdx
derivative of (tan(x)^{sec(x)})	\frac{d}{dx}((\tan(x))^{\sec(x)})
integral of tan^2(y)+1	\int\:\tan^{2}(y)+1dy
(\partial)/(\partial x)(2x^2+y^2-4y+4)	\frac{\partial\:}{\partial\:x}(2x^{2}+y^{2}-4y+4)
area 0.5(e^x+e^{-x}),0<= x<= ln(2)	area\:0.5(e^{x}+e^{-x}),0\le\:x\le\:\ln(2)
derivative of (log_{10}(x)/(ln(x))+2x)	\frac{d}{dx}(\frac{\log_{10}(x)}{\ln(x)}+2x)
y^{''}+5y^'+6y=2e^x	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=2e^{x}
derivative of in(sec(x))	\frac{d}{dx}(in(\sec(x)))
sum from n=1 to infinity of 2/(e^{n-3)}	\sum\:_{n=1}^{\infty\:}\frac{2}{e^{n-3}}
y^{''}-2/x y^'-4/(x^2)y=3x^2	y^{\prime\:\prime\:}-\frac{2}{x}y^{\prime\:}-\frac{4}{x^{2}}y=3x^{2}
limit as x approaches 1+of x^3-4	\lim\:_{x\to\:1+}(x^{3}-4)
limit as x approaches-1 of (2x)/(x+1)	\lim\:_{x\to\:-1}(\frac{2x}{x+1})
sum from n=1 to infinity of 3/(n^4)	\sum\:_{n=1}^{\infty\:}\frac{3}{n^{4}}
derivative of 1/(arctan(x))	\frac{d}{dx}(\frac{1}{\arctan(x)})
limit as h approaches 0 of ((1+h)^2-1)/h	\lim\:_{h\to\:0}(\frac{(1+h)^{2}-1}{h})
limit as x approaches 1 of 1+6x^2	\lim\:_{x\to\:1}(1+6x^{2})
tangent of y=(-8x)/(x^2+1),(1,-4)	tangent\:y=\frac{-8x}{x^{2}+1},(1,-4)

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