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Popular Calculus Problems

integral of x/((x^2+4x+5)^2)	\int\:\frac{x}{(x^{2}+4x+5)^{2}}dx
x^{''}+3x^'+4x=0	x^{\prime\:\prime\:}+3x^{\prime\:}+4x=0
derivative of x^2+y^4	\frac{d}{dx}(x^{2}+y^{4})
tangent of f(x)=(2x-1)/(x+7),\at x=2	tangent\:f(x)=\frac{2x-1}{x+7},\at\:x=2
tangent of f(x)= 1/(2sqrt(x)),\at x=100	tangent\:f(x)=\frac{1}{2\sqrt{x}},\at\:x=100
derivative of sin(e^{-2q})	derivative\:\sin(e^{-2q})
integral of (cos^2(2x))	\int\:(\cos^{2}(2x))dx
(\partial)/(\partial y)(x^2ye^x)	\frac{\partial\:}{\partial\:y}(x^{2}ye^{x})
slope of (0)(2.6)	slope\:(0)(2.6)
sum from n=1 to infinity of 4(1/4)^n	\sum\:_{n=1}^{\infty\:}4(\frac{1}{4})^{n}
(\partial)/(\partial z)(z^2+x^2)	\frac{\partial\:}{\partial\:z}(z^{2}+x^{2})
integral of e^{-x^2}x	\int\:e^{-x^{2}}xdx
derivative of-cos(3x3)	\frac{d}{dx}(-\cos(3x)3)
derivative of f(x)=a^2+cos^2(x)	derivative\:f(x)=a^{2}+\cos^{2}(x)
integral of e^{y^2}y^3	\int\:e^{y^{2}}y^{3}dy
derivative of (7x+6)^2	derivative\:(7x+6)^{2}
integral of 8x^{1/3}-4x^{-1/3}	\int\:8x^{\frac{1}{3}}-4x^{-\frac{1}{3}}dx
limit as x approaches-infinity of (2e^{-1/2 x})/(x^3)	\lim\:_{x\to\:-\infty\:}(\frac{2e^{-\frac{1}{2}x}}{x^{3}})
integral of 2cos^5(x)sin^4(x)	\int\:2\cos^{5}(x)\sin^{4}(x)dx
tangent of f(x)=-(9x^2)/2+8x-22	tangent\:f(x)=-\frac{9x^{2}}{2}+8x-22
(dh)/(dt)=-h^{1/3}	\frac{dh}{dt}=-h^{\frac{1}{3}}
integral of (x^2)^{23}x^2)^2	\int\:(x^{2})^{23}d(x^{2})^{2}
derivative of xe^e	derivative\:xe^{e}
derivative of y=-2x	derivative\:y=-2x
derivative of 5e^{-x^2}	derivative\:5e^{-x^{2}}
integral of ((2z-5)/7)	\int\:(\frac{2z-5}{7})dz
derivative of e^{-(x/2 ^2})	\frac{d}{dx}(e^{-(\frac{x}{2})^{2}})
integral from 0 to 1 of y/(e^{3y)}	\int\:_{0}^{1}\frac{y}{e^{3y}}dy
(dy)/(dx)=x+2y	\frac{dy}{dx}=x+2y
integral of e^6θsin(7θ)	\int\:e^{6}θ\sin(7θ)dθ
d/(dy)(3y^2)	\frac{d}{dy}(3y^{2})
derivative of (cos^2(x)dx)	\frac{d}{dx}((\cos^{2}(x))dx)
limit as x approaches 0-of-1/(x^3)	\lim\:_{x\to\:0-}(-\frac{1}{x^{3}})
integral from 5 to 10 of y/(y^2-y-2)	\int\:_{5}^{10}\frac{y}{y^{2}-y-2}dy
derivative of 8sec(x)	derivative\:8\sec(x)
limit as x approaches-a of x	\lim\:_{x\to\:-a}(x)
derivative of (x/(x+5)^4)	\frac{d}{dx}((\frac{x}{x+5})^{4})
integral of ((x+1)(3x-2))	\int\:((x+1)(3x-2))dx
integral of sin^4(x/2)	\int\:\sin^{4}(\frac{x}{2})dx
limit as x approaches 4 of x^2+2x-13	\lim\:_{x\to\:4}(x^{2}+2x-13)
limit as x approaches 1+of (x-1)^{1/2}	\lim\:_{x\to\:1+}((x-1)^{\frac{1}{2}})
(\partial}{\partial x}(\frac{(x+y))/z)	\frac{\partial\:}{\partial\:x}(\frac{(x+y)}{z})
integral of-4e^{-x}	\int\:-4e^{-x}dx
(22+x^2)y^'-2xy=0	(22+x^{2})y^{\prime\:}-2xy=0
integral of (x^2)/((x^3+1))	\int\:\frac{x^{2}}{(x^{3}+1)}dx
(dr)/(dθ)=pisin(piθ),r(1)=3	\frac{dr}{dθ}=π\sin(πθ),r(1)=3
laplacetransform (-4/3)e^{-2t}+(-2/3)e^t	laplacetransform\:(-\frac{4}{3})\cdot\:e^{-2t}+(-\frac{2}{3})\cdot\:e^{t}
laplacetransform cos(t+1)	laplacetransform\:\cos(t+1)
integral of (x^2+x)/(x^2+x+1)	\int\:\frac{x^{2}+x}{x^{2}+x+1}dx
integral of 1/(7-4x)	\int\:\frac{1}{7-4x}dx
derivative of y=e^{-11x}	derivative\:y=e^{-11x}
sum from n=1 to infinity of n^3	\sum\:_{n=1}^{\infty\:}n^{3}
(dx)/(dt)=3t^2	\frac{dx}{dt}=3t^{2}
integral of 1/(1-3t)	\int\:\frac{1}{1-3t}dt
y^'+7y=t+e^{-5t}	y^{\prime\:}+7y=t+e^{-5t}
(\partial)/(\partial x)((n-1)(1/x-1/y))	\frac{\partial\:}{\partial\:x}((n-1)(\frac{1}{x}-\frac{1}{y}))
integral of 1/((x+4)^2(x-1))	\int\:\frac{1}{(x+4)^{2}(x-1)}dx
limit as x approaches 0 of (e^x)/(x^3)	\lim\:_{x\to\:0}(\frac{e^{x}}{x^{3}})
integral of (3x-1)^5	\int\:(3x-1)^{5}dx
limit as x approaches 0+of (x^3)/(ln(x))	\lim\:_{x\to\:0+}(\frac{x^{3}}{\ln(x)})
laplacetransform t*e^{-3t}	laplacetransform\:t\cdot\:e^{-3t}
(\partial)/(\partial x)(-2xsin(x^2+y^2))	\frac{\partial\:}{\partial\:x}(-2x\sin(x^{2}+y^{2}))
limit as x approaches 3 of e^{3/(3-x)}	\lim\:_{x\to\:3}(e^{\frac{3}{3-x}})
integral from a to b of 1/(b-a)x	\int\:_{a}^{b}\frac{1}{b-a}xdx
integral of (e^x-2x^2)	\int\:(e^{x}-2x^{2})dx
xy^'=x^2+3y	xy^{\prime\:}=x^{2}+3y
integral of (1-2x)^5	\int\:(1-2x)^{5}dx
area y=e^x,y=7e^{-x},x=0	area\:y=e^{x},y=7e^{-x},x=0
integral of ln(x+sqrt(x^2-1))	\int\:\ln(x+\sqrt{x^{2}-1})dx
y^'=-100y+101cos(t)+99sin(t),y(0)=1	y^{\prime\:}=-100y+101\cos(t)+99\sin(t),y(0)=1
integral of (1/x-2/(9x^2+1))	\int\:(\frac{1}{x}-\frac{2}{9x^{2}+1})dx
derivative of (5x+1^3)	\frac{d}{dx}((5x+1)^{3})
slope ofintercept (9.1)(6.5)	slopeintercept\:(9.1)(6.5)
integral of 3/y-1/(y+3)	\int\:\frac{3}{y}-\frac{1}{y+3}dy
derivative of e^ysin(x)	\frac{d}{dx}(e^{y}\sin(x))
integral of 3/(xsqrt(1+2x))	\int\:\frac{3}{x\sqrt{1+2x}}dx
integral of 5x(sin(x))	\int\:5x(\sin(x))dx
derivative of 2sec(x+cot(x))	\frac{d}{dx}(2\sec(x)+\cot(x))
integral of (x+1)/x	\int\:\frac{x+1}{x}dx
derivative of ln(arcsin(cos(x)))	\frac{d}{dx}(\ln(\arcsin(\cos(x))))
(dy)/(dx)+4y=11	\frac{dy}{dx}+4y=11
integral of ((x^2-1))/(x^{3/2)}	\int\:\frac{(x^{2}-1)}{x^{\frac{3}{2}}}dx
derivative of sqrt(a-x)	\frac{d}{dx}(\sqrt{a-x})
integral of x6^x	\int\:x6^{x}dx
limit as x approaches 9+of (5x)/(x-9)	\lim\:_{x\to\:9+}(\frac{5x}{x-9})
integral of (-2x)	\int\:(-2x)dx
(d^4)/(dx^4)(1/(1+x))	\frac{d^{4}}{dx^{4}}(\frac{1}{1+x})
f(x)=(ln(x)-1)/(ln^2(x))	f(x)=\frac{\ln(x)-1}{\ln^{2}(x)}
derivative of f(x)=(x^2-3x)/(x+1)	derivative\:f(x)=\frac{x^{2}-3x}{x+1}
y^{''}-y^'+y=0	y^{\prime\:\prime\:}-y^{\prime\:}+y=0
implicit (dy)/(dx),x^8-y=0	implicit\:\frac{dy}{dx},x^{8}-y=0
integral of xsin(4x)	\int\:x\sin(4x)dx
(\partial)/(\partial x)((y/x)*ln(x))	\frac{\partial\:}{\partial\:x}((\frac{y}{x})\cdot\:\ln(x))
limit as x approaches 0 of x/(x-4)	\lim\:_{x\to\:0}(\frac{x}{x-4})
y^{''}+4y^'+13y=0,y(0)=3,y^'(0)=-12	y^{\prime\:\prime\:}+4y^{\prime\:}+13y=0,y(0)=3,y^{\prime\:}(0)=-12
limit as x approaches 2 of sqrt(x-5)	\lim\:_{x\to\:2}(\sqrt{x-5})
integral from 0 to 2 of 1/((2x-1)^{2/3)}	\int\:_{0}^{2}\frac{1}{(2x-1)^{\frac{2}{3}}}dx
(\partial)/(\partial x)(x^4+3y^2-x)	\frac{\partial\:}{\partial\:x}(x^{4}+3y^{2}-x)
derivative of (x^2-4)/(x-2)	derivative\:\frac{x^{2}-4}{x-2}
derivative of x+y+2	\frac{d}{dx}(x+y+2)

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