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Popular Calculus Problems

integral of ln((sqrt(x))/(1+sqrt(x)))	\int\:\ln(\frac{\sqrt{x}}{1+\sqrt{x}})dx
derivative of 2x^2cos(xcot(x))	\frac{d}{dx}(2x^{2}\cos(x)\cot(x))
implicit (dy)/(dx),xy-8=0	implicit\:\frac{dy}{dx},xy-8=0
derivative of \sqrt[3]{a+bx^3}	\frac{d}{dx}(\sqrt[3]{a+bx^{3}})
tangent of f(x)=5sqrt(x)	tangent\:f(x)=5\sqrt{x}
integral from 1 to 4 of sqrt(x)(1+x)	\int\:_{1}^{4}\sqrt{x}(1+x)dx
derivative of 1/(\sqrt[3]{x^2})	\frac{d}{dx}(\frac{1}{\sqrt[3]{x^{2}}})
derivative of sin^4(x)	derivative\:\sin^{4}(x)
integral of (2u^2-1)/(u^3-u)	\int\:\frac{2u^{2}-1}{u^{3}-u}du
integral from 100 to 120 of 600	\int\:_{100}^{120}600dx
(d^2)/(dx^2)(\sqrt[9]{x})	\frac{d^{2}}{dx^{2}}(\sqrt[9]{x})
integral of (8x)/(sqrt(3-4x^2))	\int\:\frac{8x}{\sqrt{3-4x^{2}}}dx
integral from 1 to 4 of (3x^2+1)	\int\:_{1}^{4}(3x^{2}+1)dx
4x-(5ysqrt(x^2+1)dy)/(dx)=0,y(0)=-10	4x-\frac{5y\sqrt{x^{2}+1}dy}{dx}=0,y(0)=-10
f(x)=(x-4)/(x^2)	f(x)=\frac{x-4}{x^{2}}
integral of (sec^3(θ))/(tan(θ))	\int\:\frac{\sec^{3}(θ)}{\tan(θ)}dθ
derivative of f(x)=16cos(2x)	derivative\:f(x)=16\cos(2x)
(e^x+y)dx+(2+x+ye^y)dy=0,y(0)=1	(e^{x}+y)dx+(2+x+ye^{y})dy=0,y(0)=1
sum from n=0 to infinity of n(n+1)x^n	\sum\:_{n=0}^{\infty\:}n\cdot\:(n+1)\cdot\:x^{n}
integral of 1/(sqrt(16+6x-x^2))	\int\:\frac{1}{\sqrt{16+6x-x^{2}}}dx
(\partial}{\partial x}(\frac{y^4)/x)	\frac{\partial\:}{\partial\:x}(\frac{y^{4}}{x})
derivative of (2t-1)(3t-3)^{-1}	derivative\:(2t-1)(3t-3)^{-1}
derivative of arcsin(x-y)	\frac{d}{dx}(\arcsin(x-y))
integral from-1 to 3 of 3x+1	\int\:_{-1}^{3}3x+1dx
tangent of y=x^2,\at x= 1/3	tangent\:y=x^{2},\at\:x=\frac{1}{3}
(\partial)/(\partial y)((5(y+2))/((x+2)^2))	\frac{\partial\:}{\partial\:y}(\frac{5(y+2)}{(x+2)^{2}})
(\partial)/(\partial x)(y^x-ln(x^4y+6x))	\frac{\partial\:}{\partial\:x}(y^{x}-\ln(x^{4}y+6x))
y^{''}+y=-3/4 sin(t)+1/4 sin(3t)	y^{\prime\:\prime\:}+y=-\frac{3}{4}\sin(t)+\frac{1}{4}\sin(3t)
(\partial)/(\partial y)(2x^2-3y^2-2x)	\frac{\partial\:}{\partial\:y}(2x^{2}-3y^{2}-2x)
(\partial)/(\partial x)(sin(x)+cos(-6y))	\frac{\partial\:}{\partial\:x}(\sin(x)+\cos(-6y))
(\partial)/(\partial x)((5xy^2)/(x^2+y^4))	\frac{\partial\:}{\partial\:x}(\frac{5xy^{2}}{x^{2}+y^{4}})
inverse oflaplace (20)/(s*(s+10))	inverselaplace\:\frac{20}{s\cdot\:(s+10)}
integral of x^3-2.5x+1	\int\:x^{3}-2.5x+1dx
limit as t approaches 7 of (sqrt((t-7)^3))/(t-7)	\lim\:_{t\to\:7}(\frac{\sqrt{(t-7)^{3}}}{t-7})
(\partial)/(\partial x)((2x-3y)^3)	\frac{\partial\:}{\partial\:x}((2x-3y)^{3})
sum from n=0 to infinity of 1/(10n+1)	\sum\:_{n=0}^{\infty\:}\frac{1}{10n+1}
integral of (x^3-x)	\int\:(x^{3}-x)dx
sum from n=1 to infinity of 3(1/2)^{n-1}	\sum\:_{n=1}^{\infty\:}3(\frac{1}{2})^{n-1}
integral of (1+e^x)^2	\int\:(1+e^{x})^{2}dx
derivative of-5t(2t^7-1)^5	derivative\:-5t(2t^{7}-1)^{5}
integral of e^{(pix)/4}	\int\:e^{\frac{πx}{4}}dx
limit as x approaches 3+of (ln(x))/(x-3)	\lim\:_{x\to\:3+}(\frac{\ln(x)}{x-3})
integral of 1/(sqrt(x^2+12x))	\int\:\frac{1}{\sqrt{x^{2}+12x}}dx
y^'=25+y^2	y^{\prime\:}=25+y^{2}
inverse oflaplace (s+2)/((s^2+4))	inverselaplace\:\frac{s+2}{(s^{2}+4)}
d/(dt)(1/3 t^3)	\frac{d}{dt}(\frac{1}{3}t^{3})
y^{''}+25y=te^{6t}	y^{\prime\:\prime\:}+25y=te^{6t}
implicit (dy)/(dx),xy=3	implicit\:\frac{dy}{dx},xy=3
derivative of e^{x+c}	\frac{d}{dx}(e^{x+c})
integral of 1/(\sqrt[3]{4x+7)}	\int\:\frac{1}{\sqrt[3]{4x+7}}dx
2y^{''}+13y^'-7y=0	2y^{\prime\:\prime\:}+13y^{\prime\:}-7y=0
integral of 1/(x^2+t^2)	\int\:\frac{1}{x^{2}+t^{2}}dx
derivative of 1/3 tan^3(x-tan(x)+x)	\frac{d}{dx}(\frac{1}{3}\tan^{3}(x)-\tan(x)+x)
derivative of f(x)=(x+9)(x^2-9)	derivative\:f(x)=(x+9)(x^{2}-9)
inverse oflaplace 6/(s^4(s-2)^2)	inverselaplace\:\frac{6}{s^{4}(s-2)^{2}}
integral of ((x+2))/(x(x^2+4))	\int\:\frac{(x+2)}{x(x^{2}+4)}dx
derivative of 2sec^2(5pix-1)	\frac{d}{dx}(2\sec^{2}(5πx-1))
derivative of 5/x+x/5	\frac{d}{dx}(\frac{5}{x}+\frac{x}{5})
(dy)/(dx)=sqrt(16x+y)-16	\frac{dy}{dx}=\sqrt{16x+y}-16
integral of xln(1/x)	\int\:x\ln(\frac{1}{x})dx
slope of (1.1)(2.4)	slope\:(1.1)(2.4)
tangent of 5x-4sqrt(x)	tangent\:5x-4\sqrt{x}
integral of 9tan^2(x)sec(x)	\int\:9\tan^{2}(x)\sec(x)dx
(\partial)/(\partial y)(sqrt(x^2+y^2)-z)	\frac{\partial\:}{\partial\:y}(\sqrt{x^{2}+y^{2}}-z)
integral of (e^{6x})/(e^{6x)+7}	\int\:\frac{e^{6x}}{e^{6x}+7}dx
integral of (2x^2)/(20-5x^3)	\int\:\frac{2x^{2}}{20-5x^{3}}dx
tangent of x+1/x	tangent\:x+\frac{1}{x}
simplify x^2In(x)	simplify\:x^{2}In(x)
integral of cos(s)	\int\:\cos(s)ds
derivative of 3sin(-5x)	derivative\:3\sin(-5x)
sum from n=1 to infinity of (70)/(7^n)	\sum\:_{n=1}^{\infty\:}\frac{70}{7^{n}}
integral of sec^4(x/2)	\int\:\sec^{4}(\frac{x}{2})dx
integral from 0 to 3 of 30(25-t^2)	\int\:_{0}^{3}30(25-t^{2})dt
limit as x approaches infinity of \|x+2\|	\lim\:_{x\to\:\infty\:}(\left\|x+2\right\|)
integral from 0 to infinity of 1/(2x+5)	\int\:_{0}^{\infty\:}\frac{1}{2x+5}dx
integral from 0 to 1 of 1/(2t^2-2t+1)	\int\:_{0}^{1}\frac{1}{2t^{2}-2t+1}dt
taylor 1/(1-x^2),0	taylor\:\frac{1}{1-x^{2}},0
derivative of-x/5	\frac{d}{dx}(-\frac{x}{5})
limit as x approaches 2 of 3x^3-5x	\lim\:_{x\to\:2}(3x^{3}-5x)
integral from 100 to 120 of (600)/x	\int\:_{100}^{120}\frac{600}{x}dx
tangent of f(x)=4x^2-x^3,\at x=1	tangent\:f(x)=4x^{2}-x^{3},\at\:x=1
(dy)/(dx)+2y=3	\frac{dy}{dx}+2y=3
limit as x approaches 0 of 1/2 x^2	\lim\:_{x\to\:0}(\frac{1}{2}x^{2})
limit as x approaches 1 of 3x+5	\lim\:_{x\to\:1}(3x+5)
derivative of 3csc(x)+7cos(x)	derivative\:3\csc(x)+7\cos(x)
integral of 7(tan^2(x)+tan^4(x))	\int\:7(\tan^{2}(x)+\tan^{4}(x))dx
y^{''}+y=t,y(0)=1,y^'(0)=-1	y^{\prime\:\prime\:}+y=t,y(0)=1,y^{\prime\:}(0)=-1
(\partial)/(\partial y)(x/(x^7-y^3))	\frac{\partial\:}{\partial\:y}(\frac{x}{x^{7}-y^{3}})
derivative of (3x^2+1/(x+2))	\frac{d}{dx}(\frac{3x^{2}+1}{x+2})
integral of (x+2)/((3+2x-x^2)^{3/2)}	\int\:\frac{x+2}{(3+2x-x^{2})^{\frac{3}{2}}}dx
derivative of ae^{bx}	\frac{d}{dx}(ae^{bx})
limit as x approaches 2 of 2x	\lim\:_{x\to\:2}(2x)
integral of (100)/(7x-16)	\int\:\frac{100}{7x-16}dx
derivative of 4/(x+2sqrt(x))	\frac{d}{dx}(\frac{4}{x+2\sqrt{x}})
f(x)=3x^{2/3}	f(x)=3x^{\frac{2}{3}}
derivative of (4x^2+6x+2)/(sqrt(x))	derivative\:\frac{4x^{2}+6x+2}{\sqrt{x}}
derivative of 3/(sqrt(6t+8))	derivative\:\frac{3}{\sqrt{6t+8}}
tangent of cos(x),\at x= pi/4	tangent\:\cos(x),\at\:x=\frac{π}{4}
derivative of ({g}(x)/(sqrt(x)))	\frac{d}{dx}(\frac{{g}(x)}{\sqrt{x}})
integral of-4y^2	\int\:-4y^{2}dy

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