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Popular Calculus Problems

partialfraction x/(1+x)	partialfraction\:\frac{x}{1+x}
integral of sin(1+x)	\int\:\sin(1+x)dx
4t(dy)/(dt)+y=t^7	4t\frac{dy}{dt}+y=t^{7}
(\partial)/(\partial x)((1+2xy^2)^3)	\frac{\partial\:}{\partial\:x}((1+2xy^{2})^{3})
(\partial)/(\partial x)(x^{-1/2})	\frac{\partial\:}{\partial\:x}(x^{-\frac{1}{2}})
integral of 5/(sqrt(x^2+2x+5))	\int\:\frac{5}{\sqrt{x^{2}+2x+5}}dx
tangent of f(x)=9+cot(x)-2csc(x),\at x=1	tangent\:f(x)=9+\cot(x)-2\csc(x),\at\:x=1
limit as t approaches 4 of t\|t-4\|	\lim\:_{t\to\:4}(t\left\|t-4\right\|)
limit as x approaches 0 of x pi/2	\lim\:_{x\to\:0}(x\frac{π}{2})
derivative of (2x)/(sqrt(x)-1)	derivative\:\frac{2x}{\sqrt{x}-1}
(\partial)/(\partial y)(ln(x^2+y^2))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y^{2}))
integral of x^2+5x-6	\int\:x^{2}+5x-6dx
derivative of 2*10^{-3}x^3+10x	\frac{d}{dx}(2\cdot\:10^{-3}x^{3}+10x)
(\partial}{\partial s}(\frac{2r+s)/t)	\frac{\partial\:}{\partial\:s}(\frac{2r+s}{t})
y^'+2/x y=-2xy^2	y^{\prime\:}+\frac{2}{x}y=-2xy^{2}
tangent of 3x^2+7x-4	tangent\:3x^{2}+7x-4
derivative of sqrt(1-289x^2)arccos(17x)	derivative\:\sqrt{1-289x^{2}}\arccos(17x)
limit as h approaches 0 of (((1/(1-(x+h)))-(1/(1-x))))/h	\lim\:_{h\to\:0}(\frac{((\frac{1}{1-(x+h)})-(\frac{1}{1-x}))}{h})
derivative of 1/((x+y))	\frac{d}{dx}(\frac{1}{(x+y)})
limit as x approaches+0+of (1+x)^{(1/x)}	\lim\:_{x\to\:+0+}((1+x)^{(\frac{1}{x})})
(dy)/(dx)=1+sqrt(y-x)	\frac{dy}{dx}=1+\sqrt{y-x}
tangent of 3x^2-6x-9,\at x=3	tangent\:3x^{2}-6x-9,\at\:x=3
(\partial)/(\partial y)((xy^2)/(x^2y^3+1))	\frac{\partial\:}{\partial\:y}(\frac{xy^{2}}{x^{2}y^{3}+1})
limit as x approaches 1 of (x+3)/(x-2)	\lim\:_{x\to\:1}(\frac{x+3}{x-2})
area 6,0,16-2x	area\:6,0,16-2x
(dy}{dx}=\frac{xy)/3	\frac{dy}{dx}=\frac{xy}{3}
derivative of x^{-2}*ln(x)	\frac{d}{dx}(x^{-2}\cdot\:\ln(x))
integral from 0 to 1 of t^2e^t	\int\:_{0}^{1}t^{2}e^{t}dt
ty^'-y=t^2e^{-t}	ty^{\prime\:}-y=t^{2}e^{-t}
integral of (-1+x)/(x^2)	\int\:\frac{-1+x}{x^{2}}dx
(\partial)/(\partial x)(3x^2y^4-4)	\frac{\partial\:}{\partial\:x}(3x^{2}y^{4}-4)
integral of 1/(sin(x)+cos(x))	\int\:\frac{1}{\sin(x)+\cos(x)}dx
integral from-1 to 1 of 1/(2x+3)	\int\:_{-1}^{1}\frac{1}{2x+3}dx
derivative of 1/3 x^{(1/2}-x^{(3/2)})	\frac{d}{dx}(\frac{1}{3}x^{(\frac{1}{2})}-x^{(\frac{3}{2})})
tangent of f(x)= 1/(sqrt(x)),\at x= 1/4	tangent\:f(x)=\frac{1}{\sqrt{x}},\at\:x=\frac{1}{4}
integral of (ln(t))	\int\:(\ln(t))dt
tangent of 8/((x^2+4))	tangent\:\frac{8}{(x^{2}+4)}
derivative of log_{2}((x-1^3))	\frac{d}{dx}(\log_{2}((x-1)^{3}))
derivative of f(x)=x*e^{-x+1}	derivative\:f(x)=x\cdot\:e^{-x+1}
tangent of 4+5x^2-2x^3	tangent\:4+5x^{2}-2x^{3}
derivative of (sin(x+cos(x))/(e^x))	\frac{d}{dx}(\frac{\sin(x)+\cos(x)}{e^{x}})
limit as x approaches 5-of 8-x-x^2	\lim\:_{x\to\:5-}(8-x-x^{2})
y^'=(x-2)/(y-2)	y^{\prime\:}=\frac{x-2}{y-2}
(\partial)/(\partial x)(2x^2+3y^2+5z^2)	\frac{\partial\:}{\partial\:x}(2x^{2}+3y^{2}+5z^{2})
slope of y=(((x+2))/((x-2)^2)),\at x=3	slope\:y=(\frac{(x+2)}{(x-2)^{2}}),\at\:x=3
derivative of (x^2-3/(e^x))	\frac{d}{dx}(\frac{x^{2}-3}{e^{x}})
derivative of f(x)=(x^2+5)^9	derivative\:f(x)=(x^{2}+5)^{9}
integral of t^3e^{t^2}	\int\:t^{3}e^{t^{2}}dt
derivative of 2+x	\frac{d}{dx}(2+x)
implicit (dy)/(dx),15x=15y+5y^3+3y^5	implicit\:\frac{dy}{dx},15x=15y+5y^{3}+3y^{5}
y^'+y/x =5*x^3	y^{\prime\:}+\frac{y}{x}=5\cdot\:x^{3}
derivative of e^{-2x}*sin(x)	\frac{d}{dx}(e^{-2x}\cdot\:\sin(x))
integral of sqrt(1+e^{2x)}	\int\:\sqrt{1+e^{2x}}dx
derivative of ln((x^2+4x+5^3))	\frac{d}{dx}(\ln((x^{2}+4x+5)^{3}))
integral of e-e^x	\int\:e-e^{x}dx
laplacetransform 1/2 sin(4t)	laplacetransform\:\frac{1}{2}\sin(4t)
xy^'+y=-3x	xy^{\prime\:}+y=-3x
integral of 1/((v+7)^3)	\int\:\frac{1}{(v+7)^{3}}dv
derivative of f(x)=x^{2pi}	derivative\:f(x)=x^{2π}
integral of (x-2)/x	\int\:\frac{x-2}{x}dx
inverse oflaplace s/((s-2)^2)	inverselaplace\:\frac{s}{(s-2)^{2}}
integral of (e^{-bx})/(1-e^{-bx)}	\int\:\frac{e^{-bx}}{1-e^{-bx}}dx
integral of (e^x)/((x+1))	\int\:\frac{e^{x}}{(x+1)}dx
derivative of f(x)=y	derivative\:f(x)=y
inverse oflaplace (-s)/(s^2+25s+30)+1/s	inverselaplace\:\frac{-s}{s^{2}+25s+30}+\frac{1}{s}
integral of e^{2x}(1-3x)	\int\:e^{2x}(1-3x)dx
limit as x approaches 4 of e^x	\lim\:_{x\to\:4}(e^{x})
d/(da)(sin(a)-cos(a))	\frac{d}{da}(\sin(a)-\cos(a))
derivative of-(sin(x))/(cos(x))	derivative\:-\frac{\sin(x)}{\cos(x)}
x^'-10x=0	x^{\prime\:}-10x=0
y^{''}-12y^'+36y=30x+2	y^{\prime\:\prime\:}-12y^{\prime\:}+36y=30x+2
integral of 12y	\int\:12ydy
derivative of f(x)= 1/(4x^2+5x)	derivative\:f(x)=\frac{1}{4x^{2}+5x}
derivative of (925+20x-0.079x^2)/(484)	derivative\:\frac{925+20x-0.079x^{2}}{484}
derivative of (csc^2(x-cot^3(x))/(tan(x^2+2x)))	\frac{d}{dx}(\frac{\csc^{2}(x)-\cot^{3}(x)}{\tan(x^{2}+2x)})
integral of x*log_{e}(x)	\int\:x\cdot\:\log_{e}(x)dx
integral from 9 to 24 of (-x+12)	\int\:_{9}^{24}(-x+12)dx
taylor ln(s)	taylor\:\ln(s)
y^'=(3y^2+4x)/(2xy)	y^{\prime\:}=\frac{3y^{2}+4x}{2xy}
integral of (x^2)/(sqrt(-4x^2-12x-5))	\int\:\frac{x^{2}}{\sqrt{-4x^{2}-12x-5}}dx
limit as x approaches 8 of ((\sqrt[3]{x}-2))/((x-8))	\lim\:_{x\to\:8}(\frac{(\sqrt[3]{x}-2)}{(x-8)})
derivative of {f}(xe^{1/({f)(x)}})	\frac{d}{dx}({f}(x)e^{\frac{1}{{f}(x)}})
f^'(x)=((5x^2-9x+8))/(7x+6)	f^{\prime\:}(x)=\frac{(5x^{2}-9x+8)}{7x+6}
(\partial)/(\partial x)(e^{-y})	\frac{\partial\:}{\partial\:x}(e^{-y})
integral of (-x-1)/(x^2+x+1)	\int\:\frac{-x-1}{x^{2}+x+1}dx
integral of x^5cos(2x)	\int\:x^{5}\cos(2x)dx
tangent of y=(1+4x)^{3/2},\at x=2	tangent\:y=(1+4x)^{\frac{3}{2}},\at\:x=2
tangent of f(x)=5-8x^2,(-2,-27)	tangent\:f(x)=5-8x^{2},(-2,-27)
(x+2y)dx+(2x-y)dy=0	(x+2y)dx+(2x-y)dy=0
y^{''}-3y^'+2y=0	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=0
sqrt(x)+sqrt(y)y^'=0	\sqrt{x}+\sqrt{y}y^{\prime\:}=0
(dy)/(dx)=((e^x))/(y^2)	\frac{dy}{dx}=\frac{(e^{x})}{y^{2}}
integral of 1/(p^2+1)	\int\:\frac{1}{p^{2}+1}dp
derivative of xe^y+y^2e^x-1/3 x+4	\frac{d}{dx}(xe^{y}+y^{2}e^{x}-\frac{1}{3}x+4)
integral of xe^{3x^2}	\int\:xe^{3x^{2}}dx
derivative of e^{ix}	\frac{d}{dx}(e^{ix})
integral of (2cos(ln(x)))/x	\int\:\frac{2\cos(\ln(x))}{x}dx
(\partial)/(\partial y)(e^{x^y})	\frac{\partial\:}{\partial\:y}(e^{x^{y}})
(\partial)/(\partial x)(sqrt((a+x)^2+y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{(a+x)^{2}+y^{2}})
integral of 5/(cos^2(x))	\int\:\frac{5}{\cos^{2}(x)}dx

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