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Popular Calculus Problems

derivative of-2/(x^2+1)	\frac{d}{dx}(-\frac{2}{x^{2}+1})
(dy)/(dx)=((x-3))/((y+1))	\frac{dy}{dx}=\frac{(x-3)}{(y+1)}
derivative of f(x)= 1/((1+x^2))	derivative\:f(x)=\frac{1}{(1+x^{2})}
derivative of (x^2-3x+2)/(-x^2-4x-4)	derivative\:\frac{x^{2}-3x+2}{-x^{2}-4x-4}
(\partial)/(\partial x)(ln(sin(x)))	\frac{\partial\:}{\partial\:x}(\ln(\sin(x)))
integral of x^2(x^3+1)^3	\int\:x^{2}(x^{3}+1)^{3}dx
integral of (x^2+x)e^{-2x}	\int\:(x^{2}+x)e^{-2x}dx
(dy)/(dx)=(x^2-y^2)/(xy),y(2)=2	\frac{dy}{dx}=\frac{x^{2}-y^{2}}{xy},y(2)=2
area 4x,x^2-5	area\:4x,x^{2}-5
integral of sex(x)	\int\:sex(x)
area f(x)=x^2-4,1,3	area\:f(x)=x^{2}-4,1,3
slope of y= 7/(sqrt(x))	slope\:y=\frac{7}{\sqrt{x}}
integral from 0 to infinity of 12e^{-6x}	\int\:_{0}^{\infty\:}12e^{-6x}dx
integral of (4sqrt(x^2+16))/(x^4)	\int\:\frac{4\sqrt{x^{2}+16}}{x^{4}}dx
integral of-sec^2((7x)/6)	\int\:-\sec^{2}(\frac{7x}{6})dx
limit as x approaches 0 of e^{-x(1-s)}	\lim\:_{x\to\:0}(e^{-x(1-s)})
limit as x approaches pi of sin(x)	\lim\:_{x\to\:π}(\sin(x))
tangent of f(x)=5sin(x)-3cos(x),\at x=pi	tangent\:f(x)=5\sin(x)-3\cos(x),\at\:x=π
integral of 5xe^{8x}	\int\:5xe^{8x}dx
integral of (e^x)/(e^x+2)	\int\:\frac{e^{x}}{e^{x}+2}dx
derivative of (5-3x/(x^2+3x))	\frac{d}{dx}(\frac{5-3x}{x^{2}+3x})
tangent of cos((pix)/2)	tangent\:\cos(\frac{πx}{2})
integral from 0 to 1 of 4xarccos(x)	\int\:_{0}^{1}4x\arccos(x)dx
integral of (13x^3)/(sqrt(2+x^2))	\int\:\frac{13x^{3}}{\sqrt{2+x^{2}}}dx
derivative of sin((pix)^3)	derivative\:\sin((πx)^{3})
x^2y^'-2xy=5y^4,y(1)= 1/4	x^{2}y^{\prime\:}-2xy=5y^{4},y(1)=\frac{1}{4}
integral from 1 to 2 of (y^3)/2+1/(2y^3)	\int\:_{1}^{2}\frac{y^{3}}{2}+\frac{1}{2y^{3}}dy
integral of (x^3+1)/(x^3-x^2-2x)	\int\:\frac{x^{3}+1}{x^{3}-x^{2}-2x}dx
integral from 0 to pi/4 of cos^2(x/3)	\int\:_{0}^{\frac{π}{4}}\cos^{2}(\frac{x}{3})dx
integral from 1 to 2 of (x^2+2x)	\int\:_{1}^{2}(x^{2}+2x)dx
tangent of f(x)=x^2+x,\at x=-1,2	tangent\:f(x)=x^{2}+x,\at\:x=-1,2
integral from-2 to 1 of (x^2-6x+12)	\int\:_{-2}^{1}(x^{2}-6x+12)dx
derivative of x/((3x-2^4))	\frac{d}{dx}(\frac{x}{(3x-2)^{4}})
integral of (sec^2(x)+7)	\int\:(\sec^{2}(x)+7)dx
tangent of f(x)=-3x^4,\at x=-1	tangent\:f(x)=-3x^{4},\at\:x=-1
integral from-2 to 3 of (x^2+4)-(-x^2-1)	\int\:_{-2}^{3}(x^{2}+4)-(-x^{2}-1)dx
limit as x approaches infinity of 8^{-x}	\lim\:_{x\to\:\infty\:}(8^{-x})
derivative of p(x)=2x^4+3x^3-6x^2+9	derivative\:p(x)=2x^{4}+3x^{3}-6x^{2}+9
derivative of 4cos(3x-3sin(4x))	\frac{d}{dx}(4\cos(3x)-3\sin(4x))
derivative of sin(x^3+3)	\frac{d}{dx}(\sin(x^{3}+3))
derivative of 9sin(x)	\frac{d}{dx}(9\sin(x))
derivative of 2x^{-1}	\frac{d}{dx}(2x^{-1})
integral from 4 to 6 of y/(y^2-3)	\int\:_{4}^{6}\frac{y}{y^{2}-3}dy
derivative of (x^3/(48)+4/x)	\frac{d}{dx}(\frac{x^{3}}{48}+\frac{4}{x})
integral of 1/(sin(x)tan(x))	\int\:\frac{1}{\sin(x)\tan(x)}dx
integral of (17)/x	\int\:\frac{17}{x}dx
inverse oflaplace 1/(as+1)	inverselaplace\:\frac{1}{as+1}
limit as x approaches 1 of (Inx)/(x-1)	\lim\:_{x\to\:1}(\frac{Inx}{x-1})
integral of ln(kx)	\int\:\ln(kx)dx
derivative of (3x^2/(2y^2))	\frac{d}{dx}(\frac{3x^{2}}{2y^{2}})
(\partial)/(\partial x)(cos(z))	\frac{\partial\:}{\partial\:x}(\cos(z))
derivative of e^{0.5}+5x-5	\frac{d}{dx}(e^{0.5}+5x-5)
y^{''}+10y+25y=0	y^{\prime\:\prime\:}+10y+25y=0
(\partial)/(\partial x)((ln(x))/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{\ln(x)}{x^{2}})
xy^'+y=3cos(x),y(pi)=0	xy^{\prime\:}+y=3\cos(x),y(π)=0
(\partial)/(\partial x)(e^x-x(sin(y)))	\frac{\partial\:}{\partial\:x}(e^{x}-x(\sin(y)))
derivative of (6x^2+4x+2)/(sqrt(x))	derivative\:\frac{6x^{2}+4x+2}{\sqrt{x}}
derivative of-x-1	\frac{d}{dx}(-x-1)
limit as x approaches+1 of (1-x)/(x^2-1)	\lim\:_{x\to\:+1}(\frac{1-x}{x^{2}-1})
integral from 0 to 1 of xe^{-6x^2}	\int\:_{0}^{1}xe^{-6x^{2}}dx
(\partial)/(\partial x)(e^{-7t}cos(pix))	\frac{\partial\:}{\partial\:x}(e^{-7t}\cos(πx))
integral of 3x^2+4x+2	\int\:3x^{2}+4x+2dx
integral of (2-x^2)	\int\:(2-x^{2})dx
integral of sin(x)sqrt(1+cos(x))	\int\:\sin(x)\sqrt{1+\cos(x)}dx
derivative of-x^2+3	\frac{d}{dx}(-x^{2}+3)
derivative of ((51ln(8)-51))/((ln(8))^2)	derivative\:\frac{(51\ln(8)-51)}{(\ln(8))^{2}}
integral of xe^{(4-x^2)}	\int\:xe^{(4-x^{2})}dx
integral of 34x	\int\:34xdx
(\partial)/(\partial x)(7e^{x^5y})	\frac{\partial\:}{\partial\:x}(7e^{x^{5}y})
integral from-1 to 1 of 1/(x^2-2x)	\int\:_{-1}^{1}\frac{1}{x^{2}-2x}dx
sum from n=1 to infinity} 2/(sqrt(n) of-2/(\sqrt{n+1))	\sum\:_{n=1}^{\infty\:}\frac{2}{\sqrt{n}}-\frac{2}{\sqrt{n+1}}
integral of (x^2)/((1-x^2)^{5/2)}	\int\:\frac{x^{2}}{(1-x^{2})^{\frac{5}{2}}}dx
inverse oflaplace (e^{-2s})/(s^2)	inverselaplace\:\frac{e^{-2s}}{s^{2}}
limit as x approaches-2 of 8	\lim\:_{x\to\:-2}(8)
derivative of f(x)=(168)/((x+4)^5)	derivative\:f(x)=\frac{168}{(x+4)^{5}}
tangent of f(x)=xe^x	tangent\:f(x)=xe^{x}
integral of ln(7x^5)	\int\:\ln(7x^{5})dx
(\partial)/(\partial x)(e^xsin(y))	\frac{\partial\:}{\partial\:x}(e^{x}\sin(y))
(dy)/(dx)-9y^2e^{-3x}=0,y(0)=10	\frac{dy}{dx}-9y^{2}e^{-3x}=0,y(0)=10
integral of (3/(2x^{1/2)}-2/(3x^{1/3)})	\int\:(\frac{3}{2x^{\frac{1}{2}}}-\frac{2}{3x^{\frac{1}{3}}})dx
derivative of 2/3 x^{3/2}+1	\frac{d}{dx}(\frac{2}{3}x^{\frac{3}{2}}+1)
derivative of x^3-3x^2-24x+32	\frac{d}{dx}(x^{3}-3x^{2}-24x+32)
inverse oflaplace 1/(0.1s+1)	inverselaplace\:\frac{1}{0.1s+1}
integral of (3e^x+sqrt(5))	\int\:(3e^{x}+\sqrt{5})dx
derivative of (8x^6-125b^9/(2x^2-5b^3))	\frac{d}{dx}(\frac{8x^{6}-125b^{9}}{2x^{2}-5b^{3}})
derivative of (2x+1)^5(x^3-x+1)^4	derivative\:(2x+1)^{5}(x^{3}-x+1)^{4}
derivative of e^x(x-5+5)	\frac{d}{dx}(e^{x}(x-5)+5)
x(dy)/(dx)-y=6x^2	x\frac{dy}{dx}-y=6x^{2}
y^{''}+2y^'-3y=e^t+e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}-3y=e^{t}+e^{-t}
integral from 0 to 64 of 1/(sqrt(64-x))	\int\:_{0}^{64}\frac{1}{\sqrt{64-x}}dx
area x,4x,-x+22	area\:x,4x,-x+22
derivative of cxln(x)	\frac{d}{dx}(cx\ln(x))
(-x^2sin(x)+2pixsin(x)-2picos(x)+2pi)^'	(-x^{2}\sin(x)+2πx\sin(x)-2π\cos(x)+2π)^{\prime\:}
derivative of sqrt((1+cos(x)/2))	\frac{d}{dx}(\sqrt{\frac{1+\cos(x)}{2}})
integral of e^xsin(6x)	\int\:e^{x}\sin(6x)dx
derivative of (x^3+2/3)	\frac{d}{dx}(\frac{x^{3}+2}{3})
integral of e^{6x}cos(2x)	\int\:e^{6x}\cos(2x)dx
derivative of 4/(\sqrt[4]{x})	\frac{d}{dx}(\frac{4}{\sqrt[4]{x}})
y^{''}+2y^'+1y=0	y^{\prime\:\prime\:}+2y^{\prime\:}+1y=0
(\partial)/(\partial y)(x/((1+2x+3y)))	\frac{\partial\:}{\partial\:y}(\frac{x}{(1+2x+3y)})

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