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Popular Calculus Problems

integral from 1 to 8 of sqrt(x)ln(x)	\int\:_{1}^{8}\sqrt{x}\ln(x)dx
limit as x approaches 0 of (\|x-1\|)/(x-1)	\lim\:_{x\to\:0}(\frac{\left\|x-1\right\|}{x-1})
f(x)=sin^2(3x+2)	f(x)=\sin^{2}(3x+2)
(e^{2x}+e^{-x})^'	(e^{2x}+e^{-x})^{\prime\:}
slope of y=-3-5x^2	slope\:y=-3-5x^{2}
laplacetransform tcos(3t)	laplacetransform\:t\cos(3t)
integral of-x^{2/3}	\int\:-x^{\frac{2}{3}}dx
integral from 0 to 24 of sqrt(6x)	\int\:_{0}^{24}\sqrt{6x}dx
tangent of f(2.1)=3x^2-4x+1,(2,0)	tangent\:f(2.1)=3x^{2}-4x+1,(2,0)
integral of cos(x)sin^3(x)	\int\:\cos(x)\sin^{3}(x)dx
derivative of (e^{y^2})/((2y+1)^5)	derivative\:\frac{e^{y^{2}}}{(2y+1)^{5}}
derivative of 2/3 x^{3/2}-1/2 x^{1/2}	\frac{d}{dx}(\frac{2}{3}x^{\frac{3}{2}}-\frac{1}{2}x^{\frac{1}{2}})
integral of ((1-2x))/(x^2)	\int\:\frac{(1-2x)}{x^{2}}dx
derivative of 1/4 e^{-x}+e^x	\frac{d}{dx}(\frac{1}{4}e^{-x}+e^{x})
derivative of f(x)=xsqrt(x+1)	derivative\:f(x)=x\sqrt{x+1}
limit as x approaches 0 of (7^x-1)/x	\lim\:_{x\to\:0}(\frac{7^{x}-1}{x})
integral of ((5+sqrt(x)+x))/x	\int\:\frac{(5+\sqrt{x}+x)}{x}dx
y^{''}+y=3sec^3(t)	y^{\prime\:\prime\:}+y=3\sec^{3}(t)
integral from-11 to-4 of 1/x	\int\:_{-11}^{-4}\frac{1}{x}dx
limit as x approaches 0-of ([x])/x	\lim\:_{x\to\:0-}(\frac{[x]}{x})
integral from 0 to 9 of pi(x-1)	\int\:_{0}^{9}π(x-1)dx
integral of 3/(x^4)sqrt(8-1/(x^3))	\int\:\frac{3}{x^{4}}\sqrt{8-\frac{1}{x^{3}}}dx
derivative of \sqrt[3]{2x+1}	\frac{d}{dx}(\sqrt[3]{2x+1})
integral of 2cos^2(x)tan^2(x)	\int\:2\cos^{2}(x)\tan^{2}(x)dx
f(x)=(ln(x))^4	f(x)=(\ln(x))^{4}
(d^2)/(dx^2)(cos(2x))	\frac{d^{2}}{dx^{2}}(\cos(2x))
integral of (x^2)/(sqrt(3-x^2))	\int\:\frac{x^{2}}{\sqrt{3-x^{2}}}dx
derivative of 5y^2(4y^2+7)^{6/5}	derivative\:5y^{2}(4y^{2}+7)^{\frac{6}{5}}
integral of sqrt(-x^2+1)	\int\:\sqrt{-x^{2}+1}dx
(\partial)/(\partial x)(10sin(x))	\frac{\partial\:}{\partial\:x}(10\sin(x))
integral of (2sech^2(t))/(tanh(t))	\int\:\frac{2\sech^{2}(t)}{\tanh(t)}dt
sum from n=1 to infinity of n/(4(n+1)!)	\sum\:_{n=1}^{\infty\:}\frac{n}{4(n+1)!}
derivative of ln((x^2(x+1))/(sqrt(x+2)))	derivative\:\ln(\frac{x^{2}(x+1)}{\sqrt{x+2}})
integral of (5+4x)/(1+x^2)	\int\:\frac{5+4x}{1+x^{2}}dx
integral of e^{-x/8}	\int\:e^{-\frac{x}{8}}dx
x^{''}+2x^'+2=0,x(0)=0,x^'(0)=1	x^{\prime\:\prime\:}+2x^{\prime\:}+2=0,x(0)=0,x^{\prime\:}(0)=1
limit as x approaches 0 of 1/(x^3-7x)	\lim\:_{x\to\:0}(\frac{1}{x^{3}-7x})
area f(x)=2x^3+3x^2-5x,-4,3	area\:f(x)=2x^{3}+3x^{2}-5x,-4,3
(\partial)/(\partial x)(x^3ln(yz))	\frac{\partial\:}{\partial\:x}(x^{3}\ln(yz))
integral of xsqrt(x-12)	\int\:x\sqrt{x-12}dx
x(dv)/(dx)= 2/v+v	x\frac{dv}{dx}=\frac{2}{v}+v
(dy)/(dx)=2y+x(e^{3x}-e^{2x})	\frac{dy}{dx}=2y+x(e^{3x}-e^{2x})
integral from 0 to pi of pi(sin(x))^2	\int\:_{0}^{π}π(\sin(x))^{2}dx
laplacetransform e^{-t}-e^{-2t}	laplacetransform\:e^{-t}-e^{-2t}
sum from n=0 to infinity of 5(2/3)^{n-1}	\sum\:_{n=0}^{\infty\:}5(\frac{2}{3})^{n-1}
limit as x approaches 0 of xcot(3x)	\lim\:_{x\to\:0}(x\cot(3x))
integral of (3x^2+4)/(x^3+4x)	\int\:\frac{3x^{2}+4}{x^{3}+4x}dx
integral of log_{e}(x)	\int\:\log_{e}(x)dx
derivative of c_{1}e^{-4x}	\frac{d}{dx}(c_{1}e^{-4x})
y^'-0.4y=29sin(x)	y^{\prime\:}-0.4y=29\sin(x)
taylor 1/((1-x)^2),0	taylor\:\frac{1}{(1-x)^{2}},0
derivative of h(t)=-16t^2+144t	derivative\:h(t)=-16t^{2}+144t
derivative of 30e^{-0.0000323h}	derivative\:30e^{-0.0000323h}
limit as x approaches 0 of-2xsin(1/x)	\lim\:_{x\to\:0}(-2x\sin(\frac{1}{x}))
(\partial)/(\partial y)(xy^2-6x^2-3y^2)	\frac{\partial\:}{\partial\:y}(xy^{2}-6x^{2}-3y^{2})
derivative of y=(8x^3+5)^{3/2}	derivative\:y=(8x^{3}+5)^{\frac{3}{2}}
area y=e^x,y=e^{-2x},x=ln(6)	area\:y=e^{x},y=e^{-2x},x=\ln(6)
derivative of-1/(x^2-1)	\frac{d}{dx}(-\frac{1}{x^{2}}-1)
derivative of (480x)/((x^2+5)^3)	derivative\:\frac{480x}{(x^{2}+5)^{3}}
derivative of ln(sqrt(x^2-5))	\frac{d}{dx}(\ln(\sqrt{x^{2}-5}))
derivative of f(x)=(x^2-8)^2	derivative\:f(x)=(x^{2}-8)^{2}
derivative of x^2Inx	\frac{d}{dx}(x^{2}Inx)
limit as n approaches infinity of-1/n	\lim\:_{n\to\:\infty\:}(-\frac{1}{n})
integral of (3x^2+1)/(x(x-1)^3)	\int\:\frac{3x^{2}+1}{x(x-1)^{3}}dx
integral of x(x+5)^4	\int\:x(x+5)^{4}dx
integral of cos^{(3)}(5x)sin^{-2}(5x)	\int\:\cos^{(3)}(5x)\sin^{-2}(5x)dx
(\partial)/(\partial x)(e^{x^5})	\frac{\partial\:}{\partial\:x}(e^{x^{5}})
(\partial)/(\partial x)(x/((1-x)^2))	\frac{\partial\:}{\partial\:x}(\frac{x}{(1-x)^{2}})
(\partial)/(\partial y)(1/(x^3-y^2))	\frac{\partial\:}{\partial\:y}(\frac{1}{x^{3}-y^{2}})
tangent of f(x)=x^2+3,\at x=1	tangent\:f(x)=x^{2}+3,\at\:x=1
limit as x approaches-10-of (x+9)/(x+10)	\lim\:_{x\to\:-10-}(\frac{x+9}{x+10})
(\partial)/(\partial x)(2e^{-y}x)	\frac{\partial\:}{\partial\:x}(2e^{-y}x)
integral of (sin(2x))/(37+cos^2(x))	\int\:\frac{\sin(2x)}{37+\cos^{2}(x)}dx
integral of x*log_{10}(x)	\int\:x\cdot\:\log_{10}(x)dx
integral of 8y-24	\int\:8y-24dy
limit as x approaches 5+of (-1)/(x^2-25)	\lim\:_{x\to\:5+}(\frac{-1}{x^{2}-25})
integral of 9θcos(θ)	\int\:9θ\cos(θ)dθ
area x^2-3,2x	area\:x^{2}-3,2x
derivative of e^x+3xe^x	derivative\:e^{x}+3xe^{x}
limit as x approaches 0+of x^{4sin(x)}	\lim\:_{x\to\:0+}(x^{4\sin(x)})
normal of y=x^2-9x,(3,-18)	normal\:y=x^{2}-9x,(3,-18)
derivative of 4(cos(x^2-2x^2sin(x^2)))	\frac{d}{dx}(4(\cos(x^{2})-2x^{2}\sin(x^{2})))
integral of sqrt(tan^3(x))sec^4(x)	\int\:\sqrt{\tan^{3}(x)}\sec^{4}(x)dx
integral of x^{-5}	\int\:x^{-5}dx
integral of (2x+1)/(x^2+6x+10)	\int\:\frac{2x+1}{x^{2}+6x+10}dx
limit as t approaches infinity of 1/(4t)	\lim\:_{t\to\:\infty\:}(\frac{1}{4t})
derivative of f(x)=(sqrt(x))/(x+6)	derivative\:f(x)=\frac{\sqrt{x}}{x+6}
simplify ln(xy)	simplify\:\ln(xy)
(\partial)/(\partial x)(y^2-e^{xy}y)	\frac{\partial\:}{\partial\:x}(y^{2}-e^{xy}y)
integral of (x+1)^4	\int\:(x+1)^{4}dx
integral of 1/(sqrt(4x^2-49))	\int\:\frac{1}{\sqrt{4x^{2}-49}}dx
integral of 2cos(4x)	\int\:2\cos(4x)dx
limit as x approaches 2+of (2-x)/(x^2-4)	\lim\:_{x\to\:2+}(\frac{2-x}{x^{2}-4})
derivative of ln(2x+4)	\frac{d}{dx}(\ln(2x+4))
integral of ln(u)	\int\:\ln(u)du
limit as x approaches infinity of (sqrt(x^2+3))/(sqrt(3x^2+1))	\lim\:_{x\to\:\infty\:}(\frac{\sqrt{x^{2}+3}}{\sqrt{3x^{2}+1}})
integral of (2x^3+x^2-5)/(x-1)	\int\:\frac{2x^{3}+x^{2}-5}{x-1}dx
(x^2+1)y^'+5x(y-1)=0,y(0)=9	(x^{2}+1)y^{\prime\:}+5x(y-1)=0,y(0)=9
sum from n=0 to infinity of q^n	\sum\:_{n=0}^{\infty\:}q^{n}
integral of (1+8v)/(-16v^2)	\int\:\frac{1+8v}{-16v^{2}}dv

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