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Popular Calculus Problems

y^{''}=6t^2	y^{\prime\:\prime\:}=6t^{2}
integral from 0 to 6 of x^3sqrt(x^2+36)	\int\:_{0}^{6}x^{3}\sqrt{x^{2}+36}dx
limit as x approaches-3-of ((x+2))/(x+3)	\lim\:_{x\to\:-3-}(\frac{(x+2)}{x+3})
x(e^{y/x}-1)y^'=e^{y/x}(y-x),y(1)=0	x(e^{\frac{y}{x}}-1)y^{\prime\:}=e^{\frac{y}{x}}(y-x),y(1)=0
derivative of (x^2+y^2ln(x+y))	\frac{d}{dx}((x^{2}+y^{2})\ln(x+y))
derivative of (sqrt(x)+3/(sqrt(x)-5))	\frac{d}{dx}(\frac{\sqrt{x}+3}{\sqrt{x}-5})
(\partial)/(\partial y)(1/2 ln(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{2}\ln(x^{2}+y^{2}))
(\partial)/(\partial x)(e^{2x})	\frac{\partial\:}{\partial\:x}(e^{2x})
integral of (8x^3-16x^2+7)/(x^2-2x)	\int\:\frac{8x^{3}-16x^{2}+7}{x^{2}-2x}dx
integral of (sec^2(x)+5)	\int\:(\sec^{2}(x)+5)dx
integral of (x^2+1)^5*x	\int\:(x^{2}+1)^{5}\cdot\:xdx
(d^3)/(dx^3)(ln(x))	\frac{d^{3}}{dx^{3}}(\ln(x))
derivative of 6/x-2/(x^3+1/(x^4))	\frac{d}{dx}(\frac{6}{x}-\frac{2}{x^{3}}+\frac{1}{x^{4}})
derivative of y=x^{-8cos(x)}	derivative\:y=x^{-8\cos(x)}
tangent of y=sin(t)+1/6 e^t,(pi, 1/6 e^pi)	tangent\:y=\sin(t)+\frac{1}{6}e^{t},(π,\frac{1}{6}e^{π})
derivative of y=x^4*x^5	\frac{d}{dx}y=x^{4}\cdot\:x^{5}
integral of ((x^2+1))/((x-8)(x-7)^2)	\int\:\frac{(x^{2}+1)}{(x-8)(x-7)^{2}}dx
derivative of x(x^2+x+1^3)	\frac{d}{dx}(x(x^{2}+x+1)^{3})
(\partial)/(\partial x)((1+x)/(x+y))	\frac{\partial\:}{\partial\:x}(\frac{1+x}{x+y})
integral of sqrt(t^2+t)	\int\:\sqrt{t^{2}+t}dt
integral of x-2y	\int\:x-2y
inverse oflaplace-1/(s(s-1)(2s+1)(s+2))	inverselaplace\:-\frac{1}{s(s-1)(2s+1)(s+2)}
integral from 0 to 7 of 2pix(7x-x^2)	\int\:_{0}^{7}2πx(7x-x^{2})dx
3(dy)/(dx)+5y=1	3\frac{dy}{dx}+5y=1
derivative of f(x)= 3/(\sqrt[4]{x^3)}	derivative\:f(x)=\frac{3}{\sqrt[4]{x^{3}}}
2y^'=e^{x/2}+y	2y^{\prime\:}=e^{\frac{x}{2}}+y
integral of 3^{2-x}	\int\:3^{2-x}dx
integral of 1/(sqrt(x^2-2x-63))	\int\:\frac{1}{\sqrt{x^{2}-2x-63}}dx
integral from 8/3 to 4 of 3t-8	\int\:_{\frac{8}{3}}^{4}3t-8dt
derivative of ln((ax+1/(ax-1)))	\frac{d}{dx}(\ln(\frac{ax+1}{ax-1}))
derivative of f(x)=3x+3/x	derivative\:f(x)=3x+\frac{3}{x}
derivative of (e^x/(1-x))	\frac{d}{dx}(\frac{e^{x}}{1-x})
derivative of f(x)=(x-2/x)	derivative\:f(x)=(x-\frac{2}{x})
derivative of ((e^x)/(1+x^2))	\frac{d}{dx}(\frac{(e^{x})}{1+x^{2}})
integral of 10e^x	\int\:10e^{x}dx
sum from n=1 to infinity of ln(n)	\sum\:_{n=1}^{\infty\:}\ln(n)
limit as x approaches b of 7(-7)	\lim\:_{x\to\:b}(7(-7))
(dx)/(dt)= 1/(xe^{t+2x)}	\frac{dx}{dt}=\frac{1}{xe^{t+2x}}
limit as a approaches 0 of ln(a)	\lim\:_{a\to\:0}(\ln(a))
sum from n=1 to infinity of (9n^7)/(n!)	\sum\:_{n=1}^{\infty\:}\frac{9n^{7}}{n!}
(dx)/(dt)=-(x^2-x),x(0)=2	\frac{dx}{dt}=-(x^{2}-x),x(0)=2
integral from 0 to 3 of \|2x-3\|	\int\:_{0}^{3}\left\|2x-3\right\|dx
y^{''}-y^'-6y=0,y(0)=2,y^'(0)=2	y^{\prime\:\prime\:}-y^{\prime\:}-6y=0,y(0)=2,y^{\prime\:}(0)=2
derivative of 5x^2-11x-6/(x^2)	derivative\:5x^{2}-11x-\frac{6}{x^{2}}
derivative of (x^2+8x+3/(sqrt(x)))	\frac{d}{dx}(\frac{x^{2}+8x+3}{\sqrt{x}})
integral from 1 to 3 of (2x^2-2x+3)	\int\:_{1}^{3}(2x^{2}-2x+3)dx
integral of sin((npix)/l)	\int\:\sin(\frac{nπx}{l})dx
integral from 0 to 3y-5 of xy^2	\int\:_{0}^{3y-5}xy^{2}dx
integral of e^{-y^2}	\int\:e^{-y^{2}}dy
tangent of y= 2/x ,(-3,-2/3)	tangent\:y=\frac{2}{x},(-3,-\frac{2}{3})
derivative of-x^3+3x^2+4	\frac{d}{dx}(-x^{3}+3x^{2}+4)
y^'y^{''}=2	y^{\prime\:}y^{\prime\:\prime\:}=2
laplacetransform e^{-2t}(3t)^2	laplacetransform\:e^{-2t}(3t)^{2}
derivative of (f(x(3x))^2+5)	\frac{d}{dx}((f(x)(3x))^{2}+5)
limit as x approaches 2 of 5x^2-3x+1	\lim\:_{x\to\:2}(5x^{2}-3x+1)
derivative of ln(xsqrt(4x-1))	\frac{d}{dx}(\ln(x\sqrt{4x-1}))
limit as x approaches+0 of (sin^2(x))/x	\lim\:_{x\to\:+0}(\frac{\sin^{2}(x)}{x})
integral from 3 to 5 of e^x	\int\:_{3}^{5}e^{x}dx
area y=-2sqrt(x),y=2sqrt(x),x=0,x=16	area\:y=-2\sqrt{x},y=2\sqrt{x},x=0,x=16
tangent of f(x)=8x^2+3x	tangent\:f(x)=8x^{2}+3x
(\partial)/(\partial x)(2y-1/x+cos(3x))	\frac{\partial\:}{\partial\:x}(2y-\frac{1}{x}+\cos(3x))
integral of x^3sqrt(x^4+9)	\int\:x^{3}\sqrt{x^{4}+9}dx
derivative of 2sin(x+3cos(x))	\frac{d}{dx}(2\sin(x)+3\cos(x))
(\partial)/(\partial y)(2xy^2-3)	\frac{\partial\:}{\partial\:y}(2xy^{2}-3)
limit as x approaches 1 of (x+4)/(x+2)	\lim\:_{x\to\:1}(\frac{x+4}{x+2})
derivative of sqrt(4+\sqrt{3x)}	\frac{d}{dx}(\sqrt{4+\sqrt{3x}})
integral of cos((mpix)/2)	\int\:\cos(\frac{mπx}{2})dx
limit as x approaches infinity of 1-2x	\lim\:_{x\to\:\infty\:}(1-2x)
derivative of e^xx+e^x	\frac{d}{dx}(e^{x}x+e^{x})
derivative of x(sin(x))	derivative\:x(\sin(x))
derivative of-1+4sin(x)	\frac{d}{dx}(-1+4\sin(x))
(\partial)/(\partial x)(2)	\frac{\partial\:}{\partial\:x}(2)
(dy)/(dx)=((3x^2+4x-4))/(2y-4)	\frac{dy}{dx}=\frac{(3x^{2}+4x-4)}{2y-4}
derivative of 2tan(θ)	derivative\:2\tan(θ)
(d^2)/(dx^2)(3-x^2)	\frac{d^{2}}{dx^{2}}(3-x^{2})
derivative of (x-1^5)	\frac{d}{dx}((x-1)^{5})
integral of xe^{-2x^2}	\int\:xe^{-2x^{2}}dx
integral of arctan(x)+C	\int\:\arctan(x)+Cdx
integral of 36arctan(sqrt(x))	\int\:36\arctan(\sqrt{x})dx
y^'+2xy+xy^4=0	y^{\prime\:}+2xy+xy^{4}=0
taylor 8/(3x+2),5	taylor\:\frac{8}{3x+2},5
integral of 1/(sqrt(t^2-4t+20))	\int\:\frac{1}{\sqrt{t^{2}-4t+20}}dt
derivative of (ln(e^x)/x)	\frac{d}{dx}(\frac{\ln(e^{x})}{x})
integral of 6x^2+3	\int\:6x^{2}+3dx
(\partial)/(\partial x)(6x+y)	\frac{\partial\:}{\partial\:x}(6x+y)
integral of x^2+1	\int\:x^{2}+1dx
derivative of (6x+4x^2/((3+4x)^2))	\frac{d}{dx}(\frac{6x+4x^{2}}{(3+4x)^{2}})
y^'+5e^{x+y}=0	y^{\prime\:}+5e^{x+y}=0
derivative of f(x)=(sqrt(x))/(4+x)	derivative\:f(x)=\frac{\sqrt{x}}{4+x}
integral of 1/((x+1)(x^2+1))	\int\:\frac{1}{(x+1)(x^{2}+1)}dx
integral of x^3sqrt(x^2-9)	\int\:x^{3}\sqrt{x^{2}-9}dx
(dy)/(dx)=2^{x-y},y(-3)=-5	\frac{dy}{dx}=2^{x-y},y(-3)=-5
integral of (4x+8)/((x+5)^2)	\int\:\frac{4x+8}{(x+5)^{2}}dx
derivative of 1/(4x^{3/4)}	derivative\:\frac{1}{4x^{\frac{3}{4}}}
slope of (-7.4)(-4.1)	slope\:(-7.4)(-4.1)
tangent of-sin(x)	tangent\:-\sin(x)
inverse oflaplace (2/(2s+1))-(1/s)	inverselaplace\:(\frac{2}{2s+1})-(\frac{1}{s})
(y^2+xy)dx-x^2dy=0	(y^{2}+xy)dx-x^{2}dy=0
integral of (1/t)	\int\:(\frac{1}{t})dt
derivative of 5+8x^{3/2}	\frac{d}{dx}(5+8x^{\frac{3}{2}})

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