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Popular Calculus Problems

integral of (a^2-x^{2/3})	\int\:(a^{2}-x^{\frac{2}{3}})dx
limit as x approaches 0+of ln(1+sin(x))	\lim\:_{x\to\:0+}(\ln(1+\sin(x)))
derivative of-3sin(2x-6cos(x))	\frac{d}{dx}(-3\sin(2x)-6\cos(x))
derivative of (8x/(x^2+4))	\frac{d}{dx}(\frac{8x}{x^{2}+4})
integral of (3t^2-4t-4)	\int\:(3t^{2}-4t-4)dt
integral from 0 to 3 of te^{-t}	\int\:_{0}^{3}te^{-t}dt
area y^2=4x,4x-3y=4	area\:y^{2}=4x,4x-3y=4
integral from 1 to 5 of x/(sqrt(2x-1))	\int\:_{1}^{5}\frac{x}{\sqrt{2x-1}}dx
limit as x approaches 0 of cos(x)+sin(x)	\lim\:_{x\to\:0}(\cos(x)+\sin(x))
(dy)/(dx)=((y^2-1))/(x^2-1),y(7)=7	\frac{dy}{dx}=\frac{(y^{2}-1)}{x^{2}-1},y(7)=7
y^'=8x^3+2 y/x	y^{\prime\:}=8x^{3}+2\frac{y}{x}
(dy)/(dt)=-2y,y(0)=2	\frac{dy}{dt}=-2y,y(0)=2
sum from n=1 to infinity of n(5/4)^n	\sum\:_{n=1}^{\infty\:}n(\frac{5}{4})^{n}
(\partial)/(\partial x)(x^3y^5)	\frac{\partial\:}{\partial\:x}(x^{3}y^{5})
sum from n=2 to infinity of 1/(n-1)-1/n	\sum\:_{n=2}^{\infty\:}\frac{1}{n-1}-\frac{1}{n}
integral of (x^2+3x-1)/(x^3+8)	\int\:\frac{x^{2}+3x-1}{x^{3}+8}dx
derivative of cos^{ln(7x}(x))	\frac{d}{dx}(\cos^{\ln(7x)}(x))
integral of 1/x (x+1)^2	\int\:\frac{1}{x}(x+1)^{2}dx
derivative of xcos(x-picos(x)+2sin(x))	\frac{d}{dx}(x\cos(x)-π\cos(x)+2\sin(x))
6y^{''}+y^'-y=0	6y^{\prime\:\prime\:}+y^{\prime\:}-y=0
integral from 0 to pi/3 of cos^3(x)	\int\:_{0}^{\frac{π}{3}}\cos^{3}(x)dx
(xy^2+x^3)dx+(y^3+x^2y)dy=0	(xy^{2}+x^{3})dx+(y^{3}+x^{2}y)dy=0
integral of 1/(x^2+2x)	\int\:\frac{1}{x^{2}+2x}dx
integral of (4-3sin(2x))^4cos(2x)	\int\:(4-3\sin(2x))^{4}\cos(2x)dx
2yy^'+2=y^2+2x	2yy^{\prime\:}+2=y^{2}+2x
derivative of (x^2/4)	\frac{d}{dx}(\frac{x^{2}}{4})
sum from n=1 to infinity of (-6)^nx^n	\sum\:_{n=1}^{\infty\:}(-6)^{n}x^{n}
integral of (x^2)/(1-2x^3)	\int\:\frac{x^{2}}{1-2x^{3}}dx
integral of x^4e^{-x}	\int\:x^{4}e^{-x}dx
tangent of f(x)=sqrt(1-x),\at x=0	tangent\:f(x)=\sqrt{1-x},\at\:x=0
limit as x approaches 0 of 5	\lim\:_{x\to\:0}(5)
(dy)/(dx)=e^y(x^2-x)	\frac{dy}{dx}=e^{y}(x^{2}-x)
integral of (sqrt(x^2-169))/x	\int\:\frac{\sqrt{x^{2}-169}}{x}dx
derivative of (-2/(x^2))	\frac{d}{dx}(\frac{-2}{x^{2}})
implicit (dy)/(dx),y=13^x	implicit\:\frac{dy}{dx},y=13^{x}
derivative of x^4-2x^2+1	\frac{d}{dx}(x^{4}-2x^{2}+1)
derivative of f(x)=8x(x^2+3)^3	derivative\:f(x)=8x(x^{2}+3)^{3}
derivative of sin^8(x)	derivative\:\sin^{8}(x)
integral of (e^{2x})/4	\int\:\frac{e^{2x}}{4}dx
(\partial)/(\partial x)(xy^2e^{3x^2y-y^2})	\frac{\partial\:}{\partial\:x}(xy^{2}e^{3x^{2}y-y^{2}})
derivative of ((sqrt(x)+x))/(x^2)	derivative\:\frac{(\sqrt{x}+x)}{x^{2}}
inverse oflaplace 8/(s-1)-3/s	inverselaplace\:\frac{8}{s-1}-\frac{3}{s}
limit as x approaches 0 of x/(x^2+4x)	\lim\:_{x\to\:0}(\frac{x}{x^{2}+4x})
sum from n=1 to infinity of (-3)^nx^n	\sum\:_{n=1}^{\infty\:}(-3)^{n}x^{n}
limit as x approaches 4-of (\|2x\|)/x	\lim\:_{x\to\:4-}(\frac{\left\|2x\right\|}{x})
derivative of-32t	derivative\:-32t
derivative of sqrt(2)cos(x)	\frac{d}{dx}(\sqrt{2}\cos(x))
integral of sqrt(1+cos(2x))	\int\:\sqrt{1+\cos(2x)}dx
(d^2y)/(dx^2)+5(dy)/(dx)+4y=0	\frac{d^{2}y}{dx^{2}}+5\frac{dy}{dx}+4y=0
(dy)/(dx)=y^2(x+1)	\frac{dy}{dx}=y^{2}(x+1)
integral of 1/(9e^y+e^{-y)}	\int\:\frac{1}{9e^{y}+e^{-y}}dy
y^{1/2}(dy)/(dx)+y^{3/2}=1	y^{\frac{1}{2}}\frac{dy}{dx}+y^{\frac{3}{2}}=1
(\partial)/(\partial x)((x^2)/(1+t^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{1+t^{2}})
limit as x approaches infinity of x*(arctan(e^x)-pi/2)	\lim\:_{x\to\:\infty\:}(x\cdot\:(\arctan(e^{x})-\frac{π}{2}))
(d^2)/(dx^2)(e^{-2x})	\frac{d^{2}}{dx^{2}}(e^{-2x})
integral of 1/((x^4-1)^2)	\int\:\frac{1}{(x^{4}-1)^{2}}dx
parity y=sqrt(x+\sqrt{x+\sqrt{x)}}	parity\:y=\sqrt{x+\sqrt{x+\sqrt{x}}}
integral of 1/(v^2+2v)	\int\:\frac{1}{v^{2}+2v}dv
derivative of-(3x+2cos(2x))	\frac{d}{dx}(-(3x+2)\cos(2x))
y^'=x^2sec(y)	y^{\prime\:}=x^{2}\sec(y)
(dy)/(dt)=-4y+3e^{-t}	\frac{dy}{dt}=-4y+3e^{-t}
y+2y^7=(y^3+6x)y^'	y+2y^{7}=(y^{3}+6x)y^{\prime\:}
integral of 1/(x^2*sqrt(x^2+1))	\int\:\frac{1}{x^{2}\cdot\:\sqrt{x^{2}+1}}dx
integral of 4xln(4x)	\int\:4x\ln(4x)dx
(dy)/(dx)=y(xy^4-1)	\frac{dy}{dx}=y(xy^{4}-1)
integral of-2x^6sin(3x)	\int\:-2x^{6}\sin(3x)dx
inverse oflaplace ((s+5))/(s^2+5s+4)	inverselaplace\:\frac{(s+5)}{s^{2}+5s+4}
y^'+7(tan(7x))y=5cos(7x)	y^{\prime\:}+7(\tan(7x))y=5\cos(7x)
integral of 5/(x^2sqrt(x^2-9))	\int\:\frac{5}{x^{2}\sqrt{x^{2}-9}}dx
(d^2)/(dx^2)(3xsin(x^2))	\frac{d^{2}}{dx^{2}}(3x\sin(x^{2}))
integral of x/(x-9)	\int\:\frac{x}{x-9}dx
derivative of sin^5(x^3)	derivative\:\sin^{5}(x^{3})
limit as x approaches 5 of \|x-5\|	\lim\:_{x\to\:5}(\left\|x-5\right\|)
integral of-2/(sqrt(100-9t^2))	\int\:-\frac{2}{\sqrt{100-9t^{2}}}dt
(\partial)/(\partial x)(sqrt(x^2+y^2-5))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+y^{2}-5})
tangent of f(x)=x^3-x,\at x=1	tangent\:f(x)=x^{3}-x,\at\:x=1
integral of 1/(sqrt(5+4x-x^2))	\int\:\frac{1}{\sqrt{5+4x-x^{2}}}dx
limit as x approaches-infinity of ((sqrt(4x^2+1)))/((2-7x))	\lim\:_{x\to\:-\infty\:}(\frac{(\sqrt{4x^{2}+1})}{(2-7x)})
xy^'+4y=-25xsin(x^5)	xy^{\prime\:}+4y=-25x\sin(x^{5})
derivative of 3/(sqrt(7x^4-5x^2+1))	\frac{d}{dx}(\frac{3}{\sqrt{7x^{4}-5x^{2}+1}})
limit as x approaches 0.1 of (e^x-1)/x	\lim\:_{x\to\:0.1}(\frac{e^{x}-1}{x})
derivative of f(x)=(6x-x^2)^{10}	derivative\:f(x)=(6x-x^{2})^{10}
derivative of sin^5(3x)	\frac{d}{dx}(\sin^{5}(3x))
y^'=4-9x^2-6x^5	y^{\prime\:}=4-9x^{2}-6x^{5}
derivative of cos(x+sin(x)+1/2 x^2+1/x)	\frac{d}{dx}(\cos(x)+\sin(x)+\frac{1}{2}x^{2}+\frac{1}{x})
integral of (3^x+2/x)	\int\:(3^{x}+\frac{2}{x})dx
integral from 2 to 5 of 1/(sqrt(x-1))	\int\:_{2}^{5}\frac{1}{\sqrt{x-1}}dx
integral of x/k	\int\:\frac{x}{k}dx
derivative of (4t^2-t)(t^3-8t^2+12)	derivative\:(4t^{2}-t)(t^{3}-8t^{2}+12)
limit as x approaches pi-of x/(cos(x)+1)	\lim\:_{x\to\:π-}(\frac{x}{\cos(x)+1})
integral of 1/(sqrt(z))	\int\:\frac{1}{\sqrt{z}}dz
integral of 4xln(x)	\int\:4x\ln(x)dx
y^'=xy^2	y^{\prime\:}=xy^{2}
derivative of e^xsin(xcos(x))	\frac{d}{dx}(e^{x}\sin(x)\cos(x))
area 7cos(7x),7-7cos(7x),[0, pi/7 ]	area\:7\cos(7x),7-7\cos(7x),[0,\frac{π}{7}]
derivative of 1/((3x+1^2))	\frac{d}{dx}(\frac{1}{(3x+1)^{2}})
f^'(x)=(3x^5-2)^{20}	f^{\prime\:}(x)=(3x^{5}-2)^{20}
integral of 1/(x^{4/3)}	\int\:\frac{1}{x^{\frac{4}{3}}}dx
integral from 1 to R of (ln(4x))/(x^2)	\int\:_{1}^{R}\frac{\ln(4x)}{x^{2}}dx
integral of e/pi	\int\:\frac{e}{π}dx

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