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Popular Calculus Problems

integral of 2/(2+x^2)	\int\:\frac{2}{2+x^{2}}dx
y^'=x*sqrt(y)	y^{\prime\:}=x\cdot\:\sqrt{y}
(dy)/(dt)+y/t =2	\frac{dy}{dt}+\frac{y}{t}=2
y^{''}+4y=tan(2x)	y^{\prime\:\prime\:}+4y=\tan(2x)
limit as x approaches pi/4 of cos(2x)	\lim\:_{x\to\:\frac{π}{4}}(\cos(2x))
integral of 1/(sqrt(81+x^2))	\int\:\frac{1}{\sqrt{81+x^{2}}}dx
(\partial)/(\partial y)((2x)/(y^3))	\frac{\partial\:}{\partial\:y}(\frac{2x}{y^{3}})
(dy)/(dx)=(y(ln(4y)-ln(4x)+3))/(3x)	\frac{dy}{dx}=\frac{y(\ln(4y)-\ln(4x)+3)}{3x}
laplacetransform t^{9/2}	laplacetransform\:t^{\frac{9}{2}}
integral of-1/512 sin(8x)	\int\:-\frac{1}{512}\sin(8x)dx
limit as x approaches-1 of (x^3-x)/(x-1)	\lim\:_{x\to\:-1}(\frac{x^{3}-x}{x-1})
limit as x approaches 1 of ln(3x)+e^x	\lim\:_{x\to\:1}(\ln(3x)+e^{x})
integral of \sqrt[3]{tan(8x)}sec^2(8x)	\int\:\sqrt[3]{\tan(8x)}\sec^{2}(8x)dx
limit as x approaches 2 of 2x^2+4x+a	\lim\:_{x\to\:2}(2x^{2}+4x+a)
integral of x/(16x^4-1)	\int\:\frac{x}{16x^{4}-1}dx
integral of x\sqrt[3]{4x+1}	\int\:x\sqrt[3]{4x+1}dx
derivative of (3(7-x)+5sqrt(9+x^2))/(15)	derivative\:\frac{3(7-x)+5\sqrt{9+x^{2}}}{15}
derivative of x^2tan(1/x)	\frac{d}{dx}(x^{2}\tan(\frac{1}{x}))
derivative of (x^2-2)/(2x+1)	derivative\:\frac{x^{2}-2}{2x+1}
integral of (1/(x^2-4))	\int\:(\frac{1}{x^{2}-4})dx
limit as x approaches 0 of 1/x-1/(x^2+x)	\lim\:_{x\to\:0}(\frac{1}{x}-\frac{1}{x^{2}+x})
derivative of f(x)=4+3sqrt(x)	derivative\:f(x)=4+3\sqrt{x}
derivative of 9^{4x}	\frac{d}{dx}(9^{4x})
derivative of cot^8(x)	\frac{d}{dx}(\cot^{8}(x))
integral of (x^2)/((x^2-1)^2)	\int\:\frac{x^{2}}{(x^{2}-1)^{2}}dx
integral of ln(x^4)	\int\:\ln(x^{4})dx
inverse oflaplace-1/(s^4)	inverselaplace\:-\frac{1}{s^{4}}
derivative of sin(1-1/x)	\frac{d}{dx}(\sin(1-\frac{1}{x}))
integral from 0 to pi of 16sin^4(x)	\int\:_{0}^{π}16\sin^{4}(x)dx
x^3y^'+2x^2y=-2cos(2x)y^{-1/2}	x^{3}y^{\prime\:}+2x^{2}y=-2\cos(2x)y^{-\frac{1}{2}}
integral of (9.8)t	\int\:(9.8)tdt
derivative of f(x)=(x^2+3x)(x-1)	derivative\:f(x)=(x^{2}+3x)(x-1)
derivative of 120x^3-180x^2+60	\frac{d}{dx}(120x^{3}-180x^{2}+60)
inverse oflaplace (6e^{-s})/(s(10s+1))	inverselaplace\:\frac{6e^{-s}}{s(10s+1)}
(\partial)/(\partial x)(((3))/((x+y)^3))	\frac{\partial\:}{\partial\:x}(\frac{(3)}{(x+y)^{3}})
integral of sec^3(x)tan(x)	\int\:\sec^{3}(x)\tan(x)dx
limit as x approaches (-pi/2)-of sec(x)	\lim\:_{x\to\:(-\frac{π}{2})-}(\sec(x))
(\partial)/(\partial x)(6x^2+3y^2+xy)	\frac{\partial\:}{\partial\:x}(6x^{2}+3y^{2}+xy)
slope of sqrt(7x+1)(9.8)	slope\:\sqrt{7x+1}(9.8)
f^'(x)=e^{x^2}	f^{\prime\:}(x)=e^{x^{2}}
integral of 1/(3x+4)	\int\:\frac{1}{3x+4}dx
limit as x approaches 0 of 2/(x^3)	\lim\:_{x\to\:0}(\frac{2}{x^{3}})
x^2(dy)/(dx)+y^2-xy=0	x^{2}\frac{dy}{dx}+y^{2}-xy=0
derivative of arcsec(9x)	derivative\:\arcsec(9x)
integral of 6/(xln^3(x))	\int\:\frac{6}{x\ln^{3}(x)}dx
(\partial)/(\partial y)(ln(x^5+y^5))	\frac{\partial\:}{\partial\:y}(\ln(x^{5}+y^{5}))
integral of (8+4x)/(1+x^2)	\int\:\frac{8+4x}{1+x^{2}}dx
f^'(x)=3.52x^2-30.1x+81	f^{\prime\:}(x)=3.52x^{2}-30.1x+81
derivative of (10)/(sqrt(x))	derivative\:\frac{10}{\sqrt{x}}
derivative of e^{x+8}	\frac{d}{dx}(e^{x+8})
integral of sin^7(x)cos^5(x)	\int\:\sin^{7}(x)\cos^{5}(x)dx
(\partial ^2)/(\partial x\partial y)(1/(sqrt(xy)))	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(\frac{1}{\sqrt{xy}})
integral of 1+sqrt(x)	\int\:1+\sqrt{x}dx
tangent of f(x)=1-x^2	tangent\:f(x)=1-x^{2}
integral of y(1+sqrt(3+y^2))	\int\:y(1+\sqrt{3+y^{2}})dy
sum from n=1 to infinity of 14	\sum\:_{n=1}^{\infty\:}14
derivative of 8-x	derivative\:8-x
d/(dv)(ucos(v))	\frac{d}{dv}(u\cos(v))
derivative of \|sin(x\|)	\frac{d}{dx}(\left\|\sin(x)\right\|)
derivative of f(x)=x^2ln(10-5x^2)	derivative\:f(x)=x^{2}\ln(10-5x^{2})
integral of sin(φ)cos(φ)	\int\:\sin(φ)\cos(φ)dφ
derivative of arcsin(cos(x^2))	\frac{d}{dx}(\arcsin(\cos(x^{2})))
derivative of 5*tan(2x^3+2/(x^2))	\frac{d}{dx}(5\cdot\:\tan(2x^{3})+\frac{2}{x^{2}})
derivative of (x+3e^{6x})	\frac{d}{dx}((x+3)e^{6x})
(\partial)/(\partial x)((x+y^2)*e^{-4x+2y})	\frac{\partial\:}{\partial\:x}((x+y^{2})\cdot\:e^{-4x+2y})
implicit (dy)/(dx),y=(9+x)^{1/x}	implicit\:\frac{dy}{dx},y=(9+x)^{\frac{1}{x}}
limit as x approaches 5 of (34-x^2)x	\lim\:_{x\to\:5}((34-x^{2})x)
integral of (e^{-x}-e^2)(e^x+e^{-5})	\int\:(e^{-x}-e^{2})(e^{x}+e^{-5})dx
(\partial)/(\partial x)(xe^{xy}-2y)	\frac{\partial\:}{\partial\:x}(xe^{xy}-2y)
derivative of 7xe^xcsc(x)	derivative\:7xe^{x}\csc(x)
integral of 2xln(x)	\int\:2x\ln(x)dx
integral of (8x-3)/(x^2+x+1)	\int\:\frac{8x-3}{x^{2}+x+1}dx
limit as x approaches 0+of (\|x\|)/x	\lim\:_{x\to\:0+}(\frac{\left\|x\right\|}{x})
tangent of f(x)=7+4x^2-2x^3,(2,7)	tangent\:f(x)=7+4x^{2}-2x^{3},(2,7)
y^'=((2sin(x))/(sin(y))),y(0)= pi/2	y^{\prime\:}=(\frac{2\sin(x)}{\sin(y)}),y(0)=\frac{π}{2}
integral of x/((1-x)^4)	\int\:\frac{x}{(1-x)^{4}}dx
limit as x approaches 3 of x^2-2x	\lim\:_{x\to\:3}(x^{2}-2x)
derivative of (x+1^{1/2})	\frac{d}{dx}((x+1)^{\frac{1}{2}})
derivative of y= t/((t-1)^2)	derivative\:y=\frac{t}{(t-1)^{2}}
limit as x approaches 8 of \sqrt[3]{x}	\lim\:_{x\to\:8}(\sqrt[3]{x})
tangent of f(x)= 4/(5x+1),\at x=-1	tangent\:f(x)=\frac{4}{5x+1},\at\:x=-1
(ln(sin(x)))^'	(\ln(\sin(x)))^{\prime\:}
(\partial)/(\partial x)((1x,3y,4z)*(1,2,3))	\frac{\partial\:}{\partial\:x}((1x,3y,4z)\cdot\:(1,2,3))
integral from 3 to 6 of (3x-x)^2	\int\:_{3}^{6}(3x-x)^{2}dx
integral of (x^{20}-5x^4)^3(x^{19}-x^3)	\int\:(x^{20}-5x^{4})^{3}(x^{19}-x^{3})dx
tangent of f(x)= 6/x ,\at x=4	tangent\:f(x)=\frac{6}{x},\at\:x=4
derivative of f(x)=cos(a^7+x^7)	derivative\:f(x)=\cos(a^{7}+x^{7})
integral of x/(1000)sqrt(x^2+2500)	\int\:\frac{x}{1000}\sqrt{x^{2}+2500}dx
derivative of (x-5*ln(x/5))	\frac{d}{dx}((x-5)\cdot\:\ln(\frac{x}{5}))
derivative of-(375/(x^4))	\frac{d}{dx}(-\frac{375}{x^{4}})
integral from-2 to 3 of x^2-x-6	\int\:_{-2}^{3}x^{2}-x-6dx
simplify 300x-1/2 x^2	simplify\:300x-\frac{1}{2}x^{2}
limit as x approaches 6 of x+2	\lim\:_{x\to\:6}(x+2)
derivative of (343+x)^{-1/3}	derivative\:(343+x)^{-\frac{1}{3}}
derivative of 2x+7	\frac{d}{dx}(2x+7)
integral of (x)/(x^2+y^2)	\int\:\frac{xdy}{x^{2}+y^{2}}dx
integral of (2x^3+4x^2+3x-1)/(x^2+2x+1)	\int\:\frac{2x^{3}+4x^{2}+3x-1}{x^{2}+2x+1}dx
integral of (6-72x)/(sqrt(49-36x^2))	\int\:\frac{6-72x}{\sqrt{49-36x^{2}}}dx
tangent of f(x)=(x-4)(x^2+8),(1,-27)	tangent\:f(x)=(x-4)(x^{2}+8),(1,-27)
limit as x approaches 1-of-x^2+5x+(-4)	\lim\:_{x\to\:1-}(-x^{2}+5x+(-4))

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