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Popular Calculus Problems

derivative of 3sin(x+3cos(x))	\frac{d}{dx}(3\sin(x)+3\cos(x))
integral of ln(x+16)	\int\:\ln(x+16)dx
derivative of ln(x*ln(x))	\frac{d}{dx}(\ln(x)\cdot\:\ln(x))
integral from-1 to 1 of x/(x^2+x-6)	\int\:_{-1}^{1}\frac{x}{x^{2}+x-6}dx
integral of (x^2)/(sqrt(256-x^2))	\int\:\frac{x^{2}}{\sqrt{256-x^{2}}}dx
(tan^2(x))^'	(\tan^{2}(x))^{\prime\:}
limit as x approaches 5 of ((13-sqrt(4x^2+69)))/(x-5)	\lim\:_{x\to\:5}(\frac{(13-\sqrt{4x^{2}+69})}{x-5})
area y=-x+4,y=x^2+3x	area\:y=-x+4,y=x^{2}+3x
(\partial)/(\partial x)(arctan(y^3x))	\frac{\partial\:}{\partial\:x}(\arctan(y^{3}x))
integral of x/(sqrt(9+x^2))	\int\:\frac{x}{\sqrt{9+x^{2}}}dx
derivative of (x^2+3/(sqrt(x^2+1)))	\frac{d}{dx}(\frac{x^{2}+3}{\sqrt{x^{2}+1}})
(\partial)/(\partial y)((x^2)/(4-y^2))	\frac{\partial\:}{\partial\:y}(\frac{x^{2}}{4-y^{2}})
(\partial)/(\partial p)((p+q)/(p+r))	\frac{\partial\:}{\partial\:p}(\frac{p+q}{p+r})
derivative of 1/(d+ke^d)	derivative\:\frac{1}{d+ke^{d}}
(d^2)/(dx^2)y+36y=0	\frac{d^{2}}{dx^{2}}y+36y=0
(\partial)/(\partial x)(5e^{xy})	\frac{\partial\:}{\partial\:x}(5e^{xy})
derivative of (3x-5/(x^2+7))	\frac{d}{dx}(\frac{3x-5}{x^{2}+7})
derivative of-12e^{-2x}	\frac{d}{dx}(-12e^{-2x})
limit as x approaches 3 of (3x-9)/(x-3)	\lim\:_{x\to\:3}(\frac{3x-9}{x-3})
derivative of (tan(x)/(x^3))	\frac{d}{dx}(\frac{\tan(x)}{x^{3}})
derivative of (f(5x))^2-2	derivative\:(f(5x))^{2}-2
integral of (sec^2(1/(x^5)))/(x^6)	\int\:\frac{\sec^{2}(\frac{1}{x^{5}})}{x^{6}}dx
integral of 1/((16+x^2)^{3/2)}	\int\:\frac{1}{(16+x^{2})^{\frac{3}{2}}}dx
roots ax+b	roots\:ax+b
integral from 1 to 4 of x^2-3x+12	\int\:_{1}^{4}x^{2}-3x+12dx
derivative of (cos(x)/(x^5))	\frac{d}{dx}(\frac{\cos(x)}{x^{5}})
integral of sin^5(t)cos^7(t)	\int\:\sin^{5}(t)\cos^{7}(t)dt
derivative of arctanh(sqrt(3x))	\frac{d}{dx}(\arctanh(\sqrt{3x}))
derivative of ln((x^2)/(2x^2+3x+2))	derivative\:\ln(\frac{x^{2}}{2x^{2}+3x+2})
integral of x-sqrt(25-x^2)	\int\:x-\sqrt{25-x^{2}}dx
(\partial)/(\partial x)(2x^4+3y^3+2xy)	\frac{\partial\:}{\partial\:x}(2x^{4}+3y^{3}+2xy)
integral of (4x^2+2x-1)/(x^3+x^2)	\int\:\frac{4x^{2}+2x-1}{x^{3}+x^{2}}dx
derivative of sqrt(a)-sqrt(x)	\frac{d}{dx}(\sqrt{a}-\sqrt{x})
integral of 2sin^6(x)cos(x)	\int\:2\sin^{6}(x)\cos(x)dx
integral of ((x^3))/(sqrt(x^2+9))	\int\:\frac{(x^{3})}{\sqrt{x^{2}+9}}dx
derivative of x^{1/3}(x+3)^{2/3}	derivative\:x^{\frac{1}{3}}(x+3)^{\frac{2}{3}}
integral of 5x^{24}	\int\:5x^{24}dx
integral of 6x^{2/5}	\int\:6x^{\frac{2}{5}}dx
derivative of tan(5x)	derivative\:\tan(5x)
inverse oflaplace 2/(4(s-3)^2+64)	inverselaplace\:\frac{2}{4(s-3)^{2}+64}
integral of cos^4(5x+1)	\int\:\cos^{4}(5x+1)dx
limit as w approaches-k of (w^2+9kw+8k^2)/(w^2+kw)	\lim\:_{w\to\:-k}(\frac{w^{2}+9kw+8k^{2}}{w^{2}+kw})
derivative of-\sqrt[3]{1-2x}	\frac{d}{dx}(-\sqrt[3]{1-2x})
integral of e^{-x}*(2-x)	\int\:e^{-x}\cdot\:(2-x)dx
area y= 1/x ,y= 3/x ,y=x,y=2x	area\:y=\frac{1}{x},y=\frac{3}{x},y=x,y=2x
(d^2)/(dydx)(sin(x^2+y^2))	\frac{d^{2}}{dydx}(\sin(x^{2}+y^{2}))
integral of (e^xsqrt(e^x+2))/(e^x+6)	\int\:\frac{e^{x}\sqrt{e^{x}+2}}{e^{x}+6}dx
derivative of ln(e^{5x})	\frac{d}{dx}(\ln(e^{5x}))
integral of sin^5(x/7)cos(x/7)	\int\:\sin^{5}(\frac{x}{7})\cos(\frac{x}{7})dx
limit as x approaches 1+of x^{2/(x-1)}	\lim\:_{x\to\:1+}(x^{\frac{2}{x-1}})
(d^2)/(dx^2)(((x-3)(x^2+3x+9))/(x^3))	\frac{d^{2}}{dx^{2}}(\frac{(x-3)(x^{2}+3x+9)}{x^{3}})
integral of ((2x^2+x+4))/(x^3+4x^2)	\int\:\frac{(2x^{2}+x+4)}{x^{3}+4x^{2}}dx
derivative of x^3+6	\frac{d}{dx}(x^{3}+6)
y'(x)	y\prime\:(x)
13xy^'-2y=-(x^2)/(y^{12)}	13xy^{\prime\:}-2y=-\frac{x^{2}}{y^{12}}
integral of-1/(2x^{1/2)sqrt(-x+1)}	\int\:-\frac{1}{2x^{\frac{1}{2}}\sqrt{-x+1}}dx
derivative of y=(x^2+1)^x	derivative\:y=(x^{2}+1)^{x}
derivative of 5/(x^7)	\frac{d}{dx}(\frac{5}{x^{7}})
laplacetransform-3e^{4t}	laplacetransform\:-3e^{4t}
integral from 1 to 3 of (e^x)/(e^x-1)	\int\:_{1}^{3}\frac{e^{x}}{e^{x}-1}dx
integral of 3-te^{-t}	\int\:3-te^{-t}dt
integral of (1-3x)/(2sqrt(1-x))	\int\:\frac{1-3x}{2\sqrt{1-x}}dx
integral of 7xe^{3x}	\int\:7xe^{3x}dx
integral of sqrt(484-x^2)	\int\:\sqrt{484-x^{2}}dx
(\partial)/(\partial x)(xe^{x^2+2y^2})	\frac{\partial\:}{\partial\:x}(xe^{x^{2}+2y^{2}})
tangent of f(x)=3x^3-x^2+9,(2,29)	tangent\:f(x)=3x^{3}-x^{2}+9,(2,29)
integral of (xln(x))/((1-x^2)^{1/2)}	\int\:\frac{x\ln(x)}{(1-x^{2})^{\frac{1}{2}}}dx
inverse oflaplace 1/((s^2+0.5s+1))	inverselaplace\:\frac{1}{(s^{2}+0.5s+1)}
y^{''}-6y^'+9y=(e^{3x})/(x^2)	y^{\prime\:\prime\:}-6y^{\prime\:}+9y=\frac{e^{3x}}{x^{2}}
area x=15-y^2,x=y^2-3	area\:x=15-y^{2},x=y^{2}-3
integral from 0 to pi/8 of arctan(2x)	\int\:_{0}^{\frac{π}{8}}\arctan(2x)dx
(\partial)/(\partial w)(warctan(uv))	\frac{\partial\:}{\partial\:w}(w\arctan(uv))
y^{''}+2y-1(y^')2=y^'	y^{\prime\:\prime\:}+2y-1(y^{\prime\:})2=y^{\prime\:}
sum from n=1 to infinity of 9	\sum\:_{n=1}^{\infty\:}9
limit as x approaches 0-of \|(8x)/x \|	\lim\:_{x\to\:0-}(\left\|\frac{8x}{x}\right\|)
integral of sin((nx)/2)	\int\:\sin(\frac{nx}{2})dx
d/(dt)(e^t-1)	\frac{d}{dt}(e^{t}-1)
integral of (x^4+x)/(x+1)	\int\:\frac{x^{4}+x}{x+1}dx
tangent of 2x^3-x^2	tangent\:2x^{3}-x^{2}
laplacetransform e^{3t}sin(4t)	laplacetransform\:e^{3t}\sin(4t)
integral of sqrt(x^2+x)	\int\:\sqrt{x^{2}+x}dx
sum from n=0 to infinity of 9^n	\sum\:_{n=0}^{\infty\:}9^{n}
derivative of f(x)=(x^2)/((x^3)(x^2))	derivative\:f(x)=\frac{x^{2}}{(x^{3})(x^{2})}
integral of 1/(xsqrt(x^2-81))	\int\:\frac{1}{x\sqrt{x^{2}-81}}dx
derivative of f(t)=t^4-20t^3+112t^2	derivative\:f(t)=t^{4}-20t^{3}+112t^{2}
tangent of f(x)=arccos(x)+x,\at x=0	tangent\:f(x)=\arccos(x)+x,\at\:x=0
t(dy)/(dt)+18y= 1/t	t\frac{dy}{dt}+18y=\frac{1}{t}
tangent of f(x)=(2x-1)/(x+3),\at x=3	tangent\:f(x)=\frac{2x-1}{x+3},\at\:x=3
integral of-sin(t)	\int\:-\sin(t)dt
(\partial ^2)/(\partial x\partial y)(ln(3x^2-y^3-3))	\frac{\partial\:^{2}}{\partial\:x\partial\:y}(\ln(3x^{2}-y^{3}-3))
derivative of 9e^{-x}+e^{4x}	\frac{d}{dx}(9e^{-x}+e^{4x})
integral of ((x^3)/(x^2+1))	\int\:(\frac{x^{3}}{x^{2}+1})dx
(\partial)/(\partial z)(\sqrt[3]{xyz})	\frac{\partial\:}{\partial\:z}(\sqrt[3]{xyz})
derivative of (2x^2-1^3*(1-x^2)^{-3})	\frac{d}{dx}((2x^{2}-1)^{3}\cdot\:(1-x^{2})^{-3})
derivative of 2+x^2	\frac{d}{dx}(2+x^{2})
derivative of ((x^3+2x^3)/(sqrt(2x-4)))	\frac{d}{dx}(\frac{(x^{3}+2x)^{3}}{\sqrt{2x-4}})
derivative of 1/(cos(x))	derivative\:\frac{1}{\cos(x)}
integral of (37)/(x^3-125)	\int\:\frac{37}{x^{3}-125}dx
derivative of 3x^2sin(x)tan(x)	derivative\:3x^{2}\sin(x)\tan(x)
(dy)/(dx)-y/x =2xe^x,y(1)=2e-8	\frac{dy}{dx}-\frac{y}{x}=2xe^{x},y(1)=2e-8

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