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Popular Calculus Problems

integral of (11+u)/u	\int\:\frac{11+u}{u}du
integral from 0 to 9 of sqrt(81+x^2)	\int\:_{0}^{9}\sqrt{81+x^{2}}dx
integral of 1/(sqrt(441+x^2))	\int\:\frac{1}{\sqrt{441+x^{2}}}dx
integral of-(x^3)/4	\int\:-\frac{x^{3}}{4}dx
integral of (x^2+x)e^x	\int\:(x^{2}+x)e^{x}dx
limit as x approaches 0 of (1-9x)^{1/x}	\lim\:_{x\to\:0}((1-9x)^{\frac{1}{x}})
derivative of 4sqrt(9x^2+5)	\frac{d}{dx}(4\sqrt{9x^{2}+5})
slope of x^2+y^2	slope\:x^{2}+y^{2}
(dy}{dx}=-\frac{(2x+ln(y))y)/x	\frac{dy}{dx}=-\frac{(2x+\ln(y))y}{x}
integral of (3^4*sin^4(x)-cos^4(x))	\int\:(3^{4}\cdot\:\sin^{4}(x)-\cos^{4}(x))dx
integral of (3e^x)/(e^{2x)+4e^x+4}	\int\:\frac{3e^{x}}{e^{2x}+4e^{x}+4}dx
limit as t approaches infinity of e^t	\lim\:_{t\to\:\infty\:}(e^{t})
(\partial)/(\partial y)(xsin(x^2-y^2))	\frac{\partial\:}{\partial\:y}(x\sin(x^{2}-y^{2}))
(dy)/(dx)=(x^2-y^2)/(xy)	\frac{dy}{dx}=\frac{x^{2}-y^{2}}{xy}
limit as h approaches pi of (cos(2))/3	\lim\:_{h\to\:π}(\frac{\cos(2)}{3})
limit as x approaches-1 of 6x^2+4x-2	\lim\:_{x\to\:-1}(6x^{2}+4x-2)
limit as x approaches 1 of 5x-x^2	\lim\:_{x\to\:1}(5x-x^{2})
derivative of e-5x+e^3x	derivative\:e-5x+e^{3}x
derivative of f(x)=(2x^3+4x)/(x^2+3)	derivative\:f(x)=\frac{2x^{3}+4x}{x^{2}+3}
integral from-1 to 3 of (1+3x)	\int\:_{-1}^{3}(1+3x)dx
integral of 1/(xsqrt(10x+49))	\int\:\frac{1}{x\sqrt{10x+49}}dx
derivative of 2x^2+3x+1	\frac{d}{dx}(2x^{2}+3x+1)
integral of (5x)/(16-4x^2)	\int\:\frac{5x}{16-4x^{2}}dx
integral from 12 to 30 of 1/30	\int\:_{12}^{30}\frac{1}{30}dx
integral of pisin(pi)x	\int\:π\sin(π)xdx
derivative of 4cos^5(x)	\frac{d}{dx}(4\cos^{5}(x))
(\partial)/(\partial y)(2e^xcos(yz))	\frac{\partial\:}{\partial\:y}(2e^{x}\cos(yz))
1/3 ((dx)/(dt))-2e^{-t}=-x	\frac{1}{3}(\frac{dx}{dt})-2e^{-t}=-x
derivative of e^{2x}tan(x)	derivative\:e^{2x}\tan(x)
taylor (1-x)^{-1/2}	taylor\:(1-x)^{-\frac{1}{2}}
(dy)/(dt)+y= 1/(1+e^{2t)}	\frac{dy}{dt}+y=\frac{1}{1+e^{2t}}
integral of (4x^2+26x+48)/((x+5)(x+2)^2)	\int\:\frac{4x^{2}+26x+48}{(x+5)(x+2)^{2}}dx
derivative of sin(x/3)	\frac{d}{dx}(\sin(\frac{x}{3}))
(d^2)/(dx^2)(x^2ln(x))	\frac{d^{2}}{dx^{2}}(x^{2}\ln(x))
derivative of (3t)/(t^2+4)	derivative\:\frac{3t}{t^{2}+4}
derivative of x(3x+2^5)	\frac{d}{dx}(x(3x+2)^{5})
integral of x^2-sec^2(x)	\int\:x^{2}-\sec^{2}(x)dx
limit as x approaches infinity of (1-e-x)/(1+e^{-x)}	\lim\:_{x\to\:\infty\:}(\frac{1-e-x}{1+e^{-x}})
derivative of (e^{2x})/(x+1)	derivative\:\frac{e^{2x}}{x+1}
sum from n=6 to infinity of 1/(n^3)	\sum\:_{n=6}^{\infty\:}\frac{1}{n^{3}}
integral of 1/(sqrt(8x))	\int\:\frac{1}{\sqrt{8x}}dx
(dy}{dx}=\frac{x^6-2y)/x	\frac{dy}{dx}=\frac{x^{6}-2y}{x}
(\partial)/(\partial y)(xy^2cos(2+x^2y))	\frac{\partial\:}{\partial\:y}(xy^{2}\cos(2+x^{2}y))
inverse oflaplace 2/((s-2))	inverselaplace\:\frac{2}{(s-2)}
integral of x(4x+1)^2	\int\:x(4x+1)^{2}dx
sum from n=1 to infinity of (-1)^n(2n!)/(2^nn!n)	\sum\:_{n=1}^{\infty\:}(-1)^{n}\frac{2n!}{2^{n}n!n}
taylor f(x)=(x^2+1)*e^{x-1}	taylor\:f(x)=(x^{2}+1)\cdot\:e^{x-1}
integral of x^2sqrt(x+2)	\int\:x^{2}\sqrt{x+2}dx
y^'+2y=4cos(2x),y(1/4 pi)=3	y^{\prime\:}+2y=4\cos(2x),y(\frac{1}{4}π)=3
sum from n=6 to infinity of (7^n)/(14^n)	\sum\:_{n=6}^{\infty\:}\frac{7^{n}}{14^{n}}
integral from 0 to 2 of 3x+5	\int\:_{0}^{2}3x+5dx
integral of 1/(x^4+4)	\int\:\frac{1}{x^{4}+4}dx
derivative of y=(x^2-2sqrt(x))/x	derivative\:y=\frac{x^{2}-2\sqrt{x}}{x}
(\partial)/(\partial v)(2v)	\frac{\partial\:}{\partial\:v}(2v)
implicit (dy)/(dx),y=-4x^5	implicit\:\frac{dy}{dx},y=-4x^{5}
derivative of y=(sqrt(x)-4)/(sqrt(x)+4)	derivative\:y=\frac{\sqrt{x}-4}{\sqrt{x}+4}
integral of 10+6x+24x^2	\int\:10+6x+24x^{2}dx
derivative of-2cos^2(x)	\frac{d}{dx}(-2\cos^{2}(x))
integral from 6 to 8 of (78)/((x-6)^3)	\int\:_{6}^{8}\frac{78}{(x-6)^{3}}dx
integral of (2x^3+6x+3)/((x+2)^2(x^2+1))	\int\:\frac{2x^{3}+6x+3}{(x+2)^{2}(x^{2}+1)}dx
integral of (t^2+t)e^{t^3}+3^t	\int\:(t^{2}+t)e^{t^{3}}+3^{t}dt
limit as x approaches 0 of ln(x^2)(1e^x+1)	\lim\:_{x\to\:0}(\ln(x^{2})(1e^{x}+1))
d/(dt)(3cos^3(t))	\frac{d}{dt}(3\cos^{3}(t))
laplacetransform 3^{(-1/10 t)}	laplacetransform\:3^{(-\frac{1}{10}t)}
inverse oflaplace (-5e^{(-3s)})/((s^2-5s+6))	inverselaplace\:\frac{-5e^{(-3s)}}{(s^{2}-5s+6)}
integral of (2x^2-5)/(x^4-5x^2+6)	\int\:\frac{2x^{2}-5}{x^{4}-5x^{2}+6}dx
integral of (2x^2+2x-3)^{10}(2x+1)	\int\:(2x^{2}+2x-3)^{10}(2x+1)dx
limit as x approaches 0-of 7/x-7/(\|x\|)	\lim\:_{x\to\:0-}(\frac{7}{x}-\frac{7}{\left\|x\right\|})
integral from 0 to 1 of 1/(sqrt(1-x^2))	\int\:_{0}^{1}\frac{1}{\sqrt{1-x^{2}}}dx
tangent of x^4-17x^2+16	tangent\:x^{4}-17x^{2}+16
limit as x approaches 0 of xe^{-2x}	\lim\:_{x\to\:0}(xe^{-2x})
integral of x^{13}	\int\:x^{13}dx
integral of 8x^2+3x-5	\int\:8x^{2}+3x-5dx
y^'=4x+y,y(0)=5	y^{\prime\:}=4x+y,y(0)=5
tangent of y=-3x^2,(-4,-48)	tangent\:y=-3x^{2},(-4,-48)
integral from 0 to 1 of te^t	\int\:_{0}^{1}te^{t}dt
integral from 9 to 10 of-6	\int\:_{9}^{10}-6dx
integral from 1 to 4 of 1/x	\int\:_{1}^{4}\frac{1}{x}dx
integral of (x^2-x+10)/(x^3+5x)	\int\:\frac{x^{2}-x+10}{x^{3}+5x}dx
integral of (2x^4)/(x^3-x^2+x-1)	\int\:\frac{2x^{4}}{x^{3}-x^{2}+x-1}dx
integral of (sqrt(1-25x^2))/(x^2)	\int\:\frac{\sqrt{1-25x^{2}}}{x^{2}}dx
integral of 3(cos(x)+sin(x))/(sin(2x))	\int\:3\frac{\cos(x)+\sin(x)}{\sin(2x)}dx
derivative of e^{2x+1}	derivative\:e^{2x+1}
derivative of f(x)=5x^{-2}	derivative\:f(x)=5x^{-2}
integral of (3x-2)e-x	\int\:(3x-2)e-xdx
f^'(x)=5e^x+3x^2-2x	f^{\prime\:}(x)=5e^{x}+3x^{2}-2x
(\partial)/(\partial x)(x^2+xy^2)	\frac{\partial\:}{\partial\:x}(x^{2}+xy^{2})
integral of 1/(6sqrt(x)(5+\sqrt{x))}	\int\:\frac{1}{6\sqrt{x}(5+\sqrt{x})}dx
6y^{''}+31y=0	6y^{\prime\:\prime\:}+31y=0
limit as x approaches 4 of (x^3-6)/(x-4)	\lim\:_{x\to\:4}(\frac{x^{3}-6}{x-4})
limit as x approaches-3 of x/(x-3)	\lim\:_{x\to\:-3}(\frac{x}{x-3})
derivative of f(x)=-6x^3	derivative\:f(x)=-6x^{3}
limit as x approaches 1 of (6x^2+12x-18)/(2x-2)	\lim\:_{x\to\:1}(\frac{6x^{2}+12x-18}{2x-2})
integral from-1 to 2 of 2/((2x+4)^3)	\int\:_{-1}^{2}\frac{2}{(2x+4)^{3}}dx
(\partial)/(\partial y)(-sin(x^2y)*2yx)	\frac{\partial\:}{\partial\:y}(-\sin(x^{2}y)\cdot\:2yx)
y^{''}+8y^'+73/4 y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+\frac{73}{4}y=0
integral of 2*e^{-2x}	\int\:2\cdot\:e^{-2x}dx
limit as x approaches 6-of (\|x-6\|)/(x-6)	\lim\:_{x\to\:6-}(\frac{\left\|x-6\right\|}{x-6})
derivative of f(θ)=cot^2(sin(θ))	derivative\:f(θ)=\cot^{2}(\sin(θ))
(\partial)/(\partial y)(ln(x^2+y^4))	\frac{\partial\:}{\partial\:y}(\ln(x^{2}+y^{4}))

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