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Popular Calculus Problems

inverse oflaplace 1/(x^2+0.0184)	inverselaplace\:\frac{1}{x^{2}+0.0184}
integral of (10)/((x-1)(x^2-9))	\int\:\frac{10}{(x-1)(x^{2}-9)}dx
limit as x approaches 0-of 8-x^2	\lim\:_{x\to\:0-}(8-x^{2})
tangent of f(x)=1+cos(x),\at x= pi/2	tangent\:f(x)=1+\cos(x),\at\:x=\frac{π}{2}
(dx)/(dt)+t^5x^7+x/t =0	\frac{dx}{dt}+t^{5}x^{7}+\frac{x}{t}=0
derivative of f(x)=xcos(x)	derivative\:f(x)=x\cos(x)
integral of 1/((x+1)sqrt(x))	\int\:\frac{1}{(x+1)\sqrt{x}}dx
(\partial)/(\partial t)(1/t)	\frac{\partial\:}{\partial\:t}(\frac{1}{t})
integral of cos(In(x))	\int\:\cos(In(x))dx
derivative of 1/((1-2x^2))	\frac{d}{dx}(\frac{1}{(1-2x)^{2}})
derivative of sqrt((x^2-64/(x^2+64)))	\frac{d}{dx}(\sqrt{\frac{x^{2}-64}{x^{2}+64}})
limit as x approaches 0 of (4/(1+x)-4)/x	\lim\:_{x\to\:0}(\frac{\frac{4}{1+x}-4}{x})
(\partial)/(\partial x)((14x)/(7x^2+y^2+2))	\frac{\partial\:}{\partial\:x}(\frac{14x}{7x^{2}+y^{2}+2})
integral from 0 to 1 of 1/(sqrt(x+2))	\int\:_{0}^{1}\frac{1}{\sqrt{x+2}}dx
inverse oflaplace (7s+4)/(2s^2+16s+30)	inverselaplace\:\frac{7s+4}{2s^{2}+16s+30}
derivative of (x-2)/(x^2-4)	derivative\:\frac{x-2}{x^{2}-4}
limit as x approaches 2 of-x+2x^2-1	\lim\:_{x\to\:2}(-x+2x^{2}-1)
inverse oflaplace (10)/(s^2+2s+10)	inverselaplace\:\frac{10}{s^{2}+2s+10}
derivative of (1/(x^2)^{tan(x)})	\frac{d}{dx}((\frac{1}{x^{2}})^{\tan(x)})
tangent of 3/((4x+1))	tangent\:\frac{3}{(4x+1)}
y^'+(2/t)y=(cos(t))/(t^2)	y^{\prime\:}+(\frac{2}{t})y=\frac{\cos(t)}{t^{2}}
(\partial)/(\partial x)(4x^8y^6+6x^7y^5)	\frac{\partial\:}{\partial\:x}(4x^{8}y^{6}+6x^{7}y^{5})
derivative of x+2^x	derivative\:x+2^{x}
derivative of 9e^{x^2}	derivative\:9e^{x^{2}}
derivative of 4^{x^9}	derivative\:4^{x^{9}}
integral of (e^{-16x})	\int\:(e^{-16x})dx
integral of t^2ln(t)	\int\:t^{2}\ln(t)dt
limit as x approaches pi of csc(x+pi)	\lim\:_{x\to\:π}(\csc(x+π))
(\partial)/(\partial x)(sec^2(xy^2)y^2)	\frac{\partial\:}{\partial\:x}(\sec^{2}(xy^{2})y^{2})
inverse oflaplace (3s-5)/((s-1)^2)	inverselaplace\:\frac{3s-5}{(s-1)^{2}}
maclaurin f(x)=arctan(2x)	maclaurin\:f(x)=\arctan(2x)
integral of (2x-6)^3	\int\:(2x-6)^{3}dx
derivative of 1/(1+4x)	\frac{d}{dx}(\frac{1}{1+4x})
integral from 0 to 3 of (x+1)^{1/2}	\int\:_{0}^{3}(x+1)^{\frac{1}{2}}dx
(\partial)/(\partial x)(ln(5ye^{xy}))	\frac{\partial\:}{\partial\:x}(\ln(5ye^{xy}))
integral of (cos(x))/(2sqrt(x))	\int\:\frac{\cos(x)}{2\sqrt{x}}dx
integral of (e^x)/(49-e^{2x)}	\int\:\frac{e^{x}}{49-e^{2x}}dx
derivative of x+1/2	\frac{d}{dx}(x+\frac{1}{2})
derivative of 2/(\sqrt[3]{x^3-9})	\frac{d}{dx}(\frac{2}{\sqrt[3]{x^{3}-9}})
y^'-y=e^{-t}	y^{\prime\:}-y=e^{-t}
derivative of ((x+1)^2)/(3x-4)	derivative\:\frac{(x+1)^{2}}{3x-4}
(\partial)/(\partial x)(xe^{(y/z)})	\frac{\partial\:}{\partial\:x}(xe^{(\frac{y}{z})})
integral of sec(x)(2tan(x)-6sec(x))	\int\:\sec(x)(2\tan(x)-6\sec(x))dx
integral of (x^2+24x-4)/(x^3-4x)	\int\:\frac{x^{2}+24x-4}{x^{3}-4x}dx
(\partial)/(\partial x)(n/(x+1))	\frac{\partial\:}{\partial\:x}(\frac{n}{x+1})
limit as x approaches-5 of 5/(x+3)	\lim\:_{x\to\:-5}(\frac{5}{x+3})
(\partial)/(\partial x)(-1)	\frac{\partial\:}{\partial\:x}(-1)
integral of (3x^{11})/(x^2-x-6)	\int\:\frac{3x^{11}}{x^{2}-x-6}dx
integral of x*sqrt(x+6)	\int\:x\cdot\:\sqrt{x+6}dx
derivative of \sqrt[3]{3x^3+4x}	\frac{d}{dx}(\sqrt[3]{3x^{3}+4x})
integral of 1/((x-2)(x+3))	\int\:\frac{1}{(x-2)(x+3)}dx
integral from-infinity to 0 of 1/(4-9x)	\int\:_{-\infty\:}^{0}\frac{1}{4-9x}dx
derivative of f(x)=sqrt(x^2-4)	derivative\:f(x)=\sqrt{x^{2}-4}
integral of (x^4)/(x^2-4)	\int\:\frac{x^{4}}{x^{2}-4}dx
derivative of ln(18-x^2)	\frac{d}{dx}(\ln(18-x^{2}))
(\partial)/(\partial x)(2(y-2)^3(x-6))	\frac{\partial\:}{\partial\:x}(2\cdot\:(y-2)^{3}\cdot\:(x-6))
slope of (0.3)(2.7)	slope\:(0.3)(2.7)
4y^{''}+y=2sec(t/2)	4y^{\prime\:\prime\:}+y=2\sec(\frac{t}{2})
derivative of f(x)=(0.09(5^x))/(x^3)	derivative\:f(x)=\frac{0.09(5^{x})}{x^{3}}
(100-x^2)(dy)/(dx)=7y	(100-x^{2})\frac{dy}{dx}=7y
area 6sin(x)-6cos(2x),[0, pi/2 ]	area\:6\sin(x)-6\cos(2x),[0,\frac{π}{2}]
(\partial)/(\partial x)(-xsin(xy))	\frac{\partial\:}{\partial\:x}(-x\sin(xy))
derivative of xe^xsin(x)	\frac{d}{dx}(x\cdot\:e^{x}\cdot\:\sin(x))
integral from 8 to 10 of y/(y^2-4y-5)	\int\:_{8}^{10}\frac{y}{y^{2}-4y-5}dy
derivative of f(x)=(-2x^3+x^2-2x-1)x^3	derivative\:f(x)=(-2x^{3}+x^{2}-2x-1)x^{3}
y^{''}+64y=sin(8t)	y^{\prime\:\prime\:}+64y=\sin(8t)
limit as x approaches 0 of sqrt(x^2+4)	\lim\:_{x\to\:0}(\sqrt{x^{2}+4})
derivative of 2/(9x^3)	\frac{d}{dx}(\frac{2}{9x^{3}})
dy=x^2sin(8x)dx	dy=x^{2}\sin(8x)dx
(\partial)/(\partial y)(x^2y^3sin(x-2y))	\frac{\partial\:}{\partial\:y}(x^{2}y^{3}\sin(x-2y))
limit as x approaches 7 of x+6	\lim\:_{x\to\:7}(x+6)
y^'= x/(14y)	y^{\prime\:}=\frac{x}{14y}
integral from (3pi)/2 to 2pi of-4sin(x)	\int\:_{\frac{3π}{2}}^{2π}-4\sin(x)dx
limit as x approaches-2 of ln(x+2)	\lim\:_{x\to\:-2}(\ln(x+2))
derivative of x/(sqrt(x-4))	\frac{d}{dx}(\frac{x}{\sqrt{x-4}})
integral of e^{x+ln(x)}	\int\:e^{x+\ln(x)}dx
integral of 6sqrt(x)e^{sqrt(x)}	\int\:6\sqrt{x}e^{\sqrt{x}}dx
(\partial)/(\partial x)(x(150y+60z+240t))	\frac{\partial\:}{\partial\:x}(x(150y+60z+240t))
expand (x^4+3x^2)(-x^2+6x+7)	expand\:(x^{4}+3x^{2})(-x^{2}+6x+7)
(x/(3x+4ln(x)))^'	(\frac{x}{3x+4\ln(x)})^{\prime\:}
(\partial)/(\partial x)(sqrt(5-3x))	\frac{\partial\:}{\partial\:x}(\sqrt{5-3x})
f(x)=sin^3(2x)	f(x)=\sin^{3}(2x)
inverse oflaplace (s-10)/(s^3(s+2.5)^2)	inverselaplace\:\frac{s-10}{s^{3}(s+2.5)^{2}}
(\partial ^2)/(\partial x\partial y)(xye^{-7y})	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(xye^{-7y})
integral of (x-2)/((x^2-4x+5)^2)	\int\:\frac{x-2}{(x^{2}-4x+5)^{2}}dx
(cos(4x))^'	(\cos(4x))^{\prime\:}
integral from-2 to 3 of (48)/(x^4)	\int\:_{-2}^{3}\frac{48}{x^{4}}dx
derivative of \sqrt[3]{t}+6sqrt(t^3)	derivative\:\sqrt[3]{t}+6\sqrt{t^{3}}
integral from 0 to 4pi of sqrt(t^2+5)	\int\:_{0}^{4π}\sqrt{t^{2}+5}dt
(\partial)/(\partial x)(xsin(3y)-ze^{-2x})	\frac{\partial\:}{\partial\:x}(x\sin(3y)-ze^{-2x})
integral of (x^3)/(2x^4+1)	\int\:\frac{x^{3}}{2x^{4}+1}dx
limit as x approaches 5 of 4x-5	\lim\:_{x\to\:5}(4x-5)
derivative of f(x)=7x-x^2	derivative\:f(x)=7x-x^{2}
implicit (dy)/(dx),(e^{xy})=x+y	implicit\:\frac{dy}{dx},(e^{xy})=x+y
integral of 1/(2-sin(x))	\int\:\frac{1}{2-\sin(x)}dx
sum from n=1 to infinity of 1/(1+2+n)	\sum\:_{n=1}^{\infty\:}\frac{1}{1+2+n}
integral of ((x-3))/(x+3)	\int\:\frac{(x-3)}{x+3}dx
area x^2-11,-2	area\:x^{2}-11,-2
derivative of (sqrt(x)/4)	\frac{d}{dx}(\frac{\sqrt{x}}{4})
integral of x^{-4/3}	\int\:x^{-\frac{4}{3}}dx

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