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Popular Calculus Problems

integral from 2 to 5 of t^4ln(2t)	\int\:_{2}^{5}t^{4}\ln(2t)dt
limit as x approaches 0 of (1+4/(x^4))^x	\lim\:_{x\to\:0}((1+\frac{4}{x^{4}})^{x})
((-9x^2+12x+24)/((x^2-5x-6)^2))^'	(\frac{-9x^{2}+12x+24}{(x^{2}-5x-6)^{2}})^{\prime\:}
integral of ((x^3+36))/(x^2+36)	\int\:\frac{(x^{3}+36)}{x^{2}+36}dx
integral of 4cos(2θ)	\int\:4\cos(2θ)dθ
derivative of 2^{(3x})	\frac{d}{dx}(2^{(3x)})
integral of r^2cos(θ)	\int\:r^{2}\cos(θ)dr
derivative of sqrt(9+\sqrt{6x)}	\frac{d}{dx}(\sqrt{9+\sqrt{6x}})
derivative of 4-2x^2	\frac{d}{dx}(4-2x^{2})
derivative of x^2e^x-2xe^x+7e^x	derivative\:x^{2}e^{x}-2xe^{x}+7e^{x}
limit as x approaches-1 of x^2+3x+2	\lim\:_{x\to\:-1}(x^{2}+3x+2)
3y^{''}-14y^'+8y=0	3y^{\prime\:\prime\:}-14y^{\prime\:}+8y=0
derivative of (x^3/(4-x^2))	\frac{d}{dx}(\frac{x^{3}}{4-x^{2}})
derivative of sec(xtan(x)sqrt(x)(x+1))	\frac{d}{dx}(\sec(x)\tan(x)\sqrt{x}(x+1))
x^3(dy)/(dx)+4x^2y=e^{-x}	x^{3}\frac{dy}{dx}+4x^{2}y=e^{-x}
integral of 5sin(3x)sin(6x)	\int\:5\sin(3x)\sin(6x)dx
inverse oflaplace (15)/(3s+sqrt(3))	inverselaplace\:\frac{15}{3s+\sqrt{3}}
integral of (x^3+2x)/(x^4+4x^2+3)	\int\:\frac{x^{3}+2x}{x^{4}+4x^{2}+3}dx
(dy)/(dt)+0.7ty=7t,y(0)=7	\frac{dy}{dt}+0.7ty=7t,y(0)=7
y^{''}+2y^'+2y=sin(2x)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(2x)
derivative of (50/(x^9))	\frac{d}{dx}(\frac{50}{x^{9}})
integral of 8/(sqrt(4-x^2))	\int\:\frac{8}{\sqrt{4-x^{2}}}dx
integral of (x^2-1)/(x^3-3x+1)	\int\:\frac{x^{2}-1}{x^{3}-3x+1}dx
derivative of cos^{sin(x)}(x)	derivative\:\cos^{\sin(x)}(x)
derivative of f(x)=e^{-0.5x}(4-x)-2	derivative\:f(x)=e^{-0.5x}(4-x)-2
sum from n=1 to infinity of 5/(4n^2-1)	\sum\:_{n=1}^{\infty\:}\frac{5}{4n^{2}-1}
derivative of-3sin(6x)	\frac{d}{dx}(-3\sin(6x))
area 3x,(6x)/7 ,55-x^2	area\:3x,\frac{6x}{7},55-x^{2}
(\partial)/(\partial t)(e^{-t}cos(t))	\frac{\partial\:}{\partial\:t}(e^{-t}\cos(t))
integral of 1/(x^3+xy^2)	\int\:\frac{1}{x^{3}+xy^{2}}dy
derivative of-16sin(4x)	\frac{d}{dx}(-16\sin(4x))
derivative of ln((1+sqrt(x)/(x^3)))	\frac{d}{dx}(\ln(\frac{1+\sqrt{x}}{x^{3}}))
integral from 1/5 to 7 of 8xln(5x)	\int\:_{\frac{1}{5}}^{7}8x\ln(5x)dx
y^'+2/x y=4x	y^{\prime\:}+\frac{2}{x}y=4x
derivative of sin^2(x/2)	\frac{d}{dx}(\sin^{2}(\frac{x}{2}))
derivative of ln(7x^2+5y^2)	\frac{d}{dx}(\ln(7x^{2}+5y^{2}))
derivative of 4t^{(-1)/8}+5ln(t)+ln(5)	derivative\:4t^{\frac{-1}{8}}+5\ln(t)+\ln(5)
sum from n=1 to infinity of 3/(5^n)+2/n	\sum\:_{n=1}^{\infty\:}\frac{3}{5^{n}}+\frac{2}{n}
tangent of f(x)=3x^2-4x+1	tangent\:f(x)=3x^{2}-4x+1
area y=4,y=x^2	area\:y=4,y=x^{2}
integral of 2e^{-x/2}	\int\:2e^{-\frac{x}{2}}dx
derivative of (9-sec(x)/(tan(x)))	\frac{d}{dx}(\frac{9-\sec(x)}{\tan(x)})
sum from n=1 to infinity of (2n)/(5n-8)	\sum\:_{n=1}^{\infty\:}\frac{2n}{5n-8}
integral of (3x^2-1)^43x	\int\:(3x^{2}-1)^{4}3xdx
integral of (x^3+5)	\int\:(x^{3}+5)dx
derivative of x^2-6(3)+9	derivative\:x^{2}-6(3)+9
derivative of sqrt(3x^2+2)	derivative\:\sqrt{3x^{2}+2}
integral of x/(4x^2+1)	\int\:\frac{x}{4x^{2}+1}dx
integral of e^{t/5}	\int\:e^{\frac{t}{5}}dt
integral of ((x+3))/(x^2+8x-9)	\int\:\frac{(x+3)}{x^{2}+8x-9}dx
limit as x approaches 2-of (x^2)/(x-2)	\lim\:_{x\to\:2-}(\frac{x^{2}}{x-2})
sum from n=1 to infinity of n^3(1+n^4)	\sum\:_{n=1}^{\infty\:}n^{3}(1+n^{4})
derivative of f(x)=x*e^{2x-4},x=2	derivative\:f(x)=x\cdot\:e^{2x-4},x=2
integral of ((sin(sqrt(x))))/(sqrt(x))	\int\:\frac{(\sin(\sqrt{x}))}{\sqrt{x}}dx
slope ofintercept (3,-1),(4,7)	slopeintercept\:(3,-1),(4,7)
derivative of y= 4/(7x^2)	derivative\:y=\frac{4}{7x^{2}}
(dy)/(dx)=(3x^2)/(y^2)	\frac{dy}{dx}=\frac{3x^{2}}{y^{2}}
tangent of 6x^2+5x+8,\at x=4	tangent\:6x^{2}+5x+8,\at\:x=4
limit as x approaches 4 of sqrt(x^3+6x)	\lim\:_{x\to\:4}(\sqrt{x^{3}+6x})
limit as x approaches 2 of 3cos(x)	\lim\:_{x\to\:2}(3\cos(x))
f(x)=x^2cos(1/x)	f(x)=x^{2}\cos(\frac{1}{x})
maclaurin (1-2x)^{-2}	maclaurin\:(1-2x)^{-2}
sum from n=2 to infinity of n/(3n^3+1)	\sum\:_{n=2}^{\infty\:}\frac{n}{3n^{3}+1}
derivative of 8/(1-x)	derivative\:\frac{8}{1-x}
d/(dt)(4t^2+2t+5)	\frac{d}{dt}(4t^{2}+2t+5)
derivative of e^{cos(x}+e^{sin(y)})	\frac{d}{dx}(e^{\cos(x)}+e^{\sin(y)})
derivative of log_{3}(5x-1)	\frac{d}{dx}(\log_{3}(5x-1))
tangent of y= 5/x ,(4, 5/4)	tangent\:y=\frac{5}{x},(4,\frac{5}{4})
derivative of t^2*sqrt(t^3+2)	derivative\:t^{2}\cdot\:\sqrt{t^{3}+2}
derivative of 1/(2sqrt(r))+1/(9r^{8/9)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{9r^{\frac{8}{9}}}
derivative of 7/(1+x)	\frac{d}{dx}(\frac{7}{1+x})
sum from n=1 to infinity of 4/(n^2+1)	\sum\:_{n=1}^{\infty\:}\frac{4}{n^{2}+1}
integral of-9.8	\int\:-9.8dx
integral of 2e^{-0.2x}	\int\:2e^{-0.2x}dx
(d^2)/(dx^2)y=(4x+3)(2x^2+7x-1)	\frac{d^{2}}{dx^{2}}y=(4x+3)(2x^{2}+7x-1)
(\partial)/(\partial x)(11x^2y+8xy^3)	\frac{\partial\:}{\partial\:x}(11x^{2}y+8xy^{3})
derivative of 4-sqrt(x+7)	\frac{d}{dx}(4-\sqrt{x+7})
derivative of 1/((4x^3))	\frac{d}{dx}(\frac{1}{(4x)^{3}})
y^'=(x^8)/y	y^{\prime\:}=\frac{x^{8}}{y}
integral of x^3+5x-1	\int\:x^{3}+5x-1dx
(\partial)/(\partial x)(3x^{2/3})	\frac{\partial\:}{\partial\:x}(3x^{\frac{2}{3}})
integral from 1 to 2 of 1/(8-3x)	\int\:_{1}^{2}\frac{1}{8-3x}dx
inverse oflaplace sin(t)	inverselaplace\:\sin(t)
derivative of e^{1/x}	derivative\:e^{\frac{1}{x}}
integral of 8x^3+12x+2	\int\:8x^{3}+12x+2dx
derivative of a{r}(xc,5x)	\frac{d}{dx}(a{r}(x)c,5x)
(\partial)/(\partial x)(x^2y^2-3y)	\frac{\partial\:}{\partial\:x}(x^{2}y^{2}-3y)
integral of 3x+2	\int\:3x+2dx
area f(x)=4x+8,0,8	area\:f(x)=4x+8,0,8
sum from n=0 to infinity of (7n!)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{7n!}{2^{n}}
tangent of f(x)=1-x-x^2,\at x=0	tangent\:f(x)=1-x-x^{2},\at\:x=0
derivative of x(29-2x)(16-2x)	derivative\:x(29-2x)(16-2x)
derivative of log_{7}(x)	derivative\:\log_{7}(x)
taylor ln(x+2),-1	taylor\:\ln(x+2),-1
2xy^'-y=3x^2	2xy^{\prime\:}-y=3x^{2}
integral of 9tan(x)sec(3)(x)	\int\:9\tan(x)\sec(3)(x)dx
integral from-1 to 1 of 4/(1+x^2)	\int\:_{-1}^{1}\frac{4}{1+x^{2}}dx
f(x)=x^6e^x	f(x)=x^{6}e^{x}
derivative of sin(x)ln(8x)	derivative\:\sin(x)\ln(8x)
derivative of e^x+4	\frac{d}{dx}(e^{x}+4)

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