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Popular Calculus Problems

derivative of sin(x)ln(cos(x))	derivative\:\sin(x)\ln(\cos(x))
limit as x approaches-1 of 3x^2+4/(x^2)	\lim\:_{x\to\:-1}(3x^{2}+\frac{4}{x^{2}})
integral of-9cot(x)ln(sin(x))	\int\:-9\cot(x)\ln(\sin(x))dx
derivative of 4e^{3x^2}sin(cos(2x))	\frac{d}{dx}(4e^{3x^{2}}\sin(\cos(2x)))
derivative of sin^2(x-cos(x))	\frac{d}{dx}(\sin^{2}(x)-\cos(x))
derivative of (x^2(e^x+5)/(e^xsqrt(x)))	\frac{d}{dx}(\frac{x^{2}(e^{x}+5)}{e^{x}\sqrt{x}})
derivative of 7^x+7cos((7x/2))	\frac{d}{dx}(7^{x}+7\cos(\frac{7x}{2}))
x^2y^{''}-xy^'+y=0	x^{2}y^{\prime\:\prime\:}-xy^{\prime\:}+y=0
integral from 1 to e^5 of 1/(x(1+ln(x)))	\int\:_{1}^{e^{5}}\frac{1}{x(1+\ln(x))}dx
integral of-sin^4(x)	\int\:-\sin^{4}(x)dx
integral of (x^2-3x-5)/x	\int\:\frac{x^{2}-3x-5}{x}dx
derivative of x^2+(432/x)	\frac{d}{dx}(x^{2}+\frac{432}{x})
integral of 1/(3+sqrt(x))	\int\:\frac{1}{3+\sqrt{x}}dx
derivative of f(x)=ln(6x^3+e^x)	derivative\:f(x)=\ln(6x^{3}+e^{x})
derivative of 1/((x^2-3x^2))	\frac{d}{dx}(\frac{1}{(x^{2}-3x)^{2}})
y^'=(y-x)/x	y^{\prime\:}=\frac{y-x}{x}
(\partial)/(\partial x)(4x^5y)	\frac{\partial\:}{\partial\:x}(4x^{5}y)
(\partial)/(\partial x)((x^2-1)/(x^2+x+1))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}-1}{x^{2}+x+1})
integral of 2^r	\int\:2^{r}dr
derivative of f(x)=sqrt(3+x)	derivative\:f(x)=\sqrt{3+x}
derivative of x^2*sec(1/x)	derivative\:x^{2}\cdot\:\sec(\frac{1}{x})
integral from 1 to 3 of (4x^3+2)	\int\:_{1}^{3}(4x^{3}+2)dx
integral of 1/((2-5x)^2)	\int\:\frac{1}{(2-5x)^{2}}dx
inverse oflaplace (s+2)/(s^2+4)	inverselaplace\:\frac{s+2}{s^{2}+4}
tangent of f(x)=(3x)/(x-2),(4,6)	tangent\:f(x)=\frac{3x}{x-2},(4,6)
derivative of 4/(r^3)	derivative\:\frac{4}{r^{3}}
integral of (2x+3)/(x^2-5x+4)	\int\:\frac{2x+3}{x^{2}-5x+4}dx
integral of 1/6 x	\int\:\frac{1}{6}xdx
derivative of x/3	derivative\:\frac{x}{3}
integral of-2y^2+4x-5	\int\:-2y^{2}+4x-5dx
f(x)=sqrt(x)-4	f(x)=\sqrt{x}-4
8x+(dy)/(dx)=0	8x+\frac{dy}{dx}=0
limit as t approaches 0 of (u-ln(k))/t	\lim\:_{t\to\:0}(\frac{u-\ln(k)}{t})
integral of (x^2+2x+1)^{20}	\int\:(x^{2}+2x+1)^{20}dx
derivative of \sqrt[4]{u}	derivative\:\sqrt[4]{u}
(dy)/(dt)= t/y	\frac{dy}{dt}=\frac{t}{y}
integral of 1/(x+x^{1/3)}	\int\:\frac{1}{x+x^{\frac{1}{3}}}dx
derivative of arctan((1+x/(1-x)))	\frac{d}{dx}(\arctan(\frac{1+x}{1-x}))
tangent of f(x)=x^3,(-2,-8)	tangent\:f(x)=x^{3},(-2,-8)
integral of ((9sin(x)+4sec(x)))/(tan(x))	\int\:\frac{(9\sin(x)+4\sec(x))}{\tan(x)}dx
tangent of 2/x	tangent\:\frac{2}{x}
laplacetransform 1(t-4)	laplacetransform\:1(t-4)
limit as x approaches 0+of sin^x(x)	\lim\:_{x\to\:0+}(\sin^{x}(x))
limit as x approaches 1 of 2x^2+x-1	\lim\:_{x\to\:1}(2x^{2}+x-1)
integral of 3e^x+7sec^2(x)	\int\:3e^{x}+7\sec^{2}(x)dx
derivative of (e^x/(e^x+e^y))	\frac{d}{dx}(\frac{e^{x}}{e^{x}+e^{y}})
integral of (1-sqrt(x))/(\sqrt[3]{x)}	\int\:\frac{1-\sqrt{x}}{\sqrt[3]{x}}dx
limit as x approaches-2 of sqrt(x)	\lim\:_{x\to\:-2}(\sqrt{x})
integral of (x^2+1)/((x-9)(x-8)^2)	\int\:\frac{x^{2}+1}{(x-9)(x-8)^{2}}dx
derivative of (x^2+sqrt(x)3^x)	\frac{d}{dx}((x^{2}+\sqrt{x})3^{x})
integral from-8 to 18 of 1/(sqrt(\|2x\|))	\int\:_{-8}^{18}\frac{1}{\sqrt{\left\|2x\right\|}}dx
(\partial)/(\partial y)(3y^2+x^2-3)	\frac{\partial\:}{\partial\:y}(3y^{2}+x^{2}-3)
(d^3)/(dx^3)(e^x)	\frac{d^{3}}{dx^{3}}(e^{x})
integral of cos^4(5x+5)	\int\:\cos^{4}(5x+5)dx
integral of log_{2}(x-4)	\int\:\log_{2}(x-4)dx
derivative of (4x^2+8x+4)/(sqrt(x))	derivative\:\frac{4x^{2}+8x+4}{\sqrt{x}}
limit as x approaches 0 of ((x^3))/(x^2)	\lim\:_{x\to\:0}(\frac{(x^{3})}{x^{2}})
derivative of (7e^xx^{5/2}/2+e^xx^{7/2})	\frac{d}{dx}(\frac{7e^{x}x^{\frac{5}{2}}}{2}+e^{x}x^{\frac{7}{2}})
(\partial)/(\partial x)(xy^3)	\frac{\partial\:}{\partial\:x}(xy^{3})
derivative of arccos(e^{7x})	derivative\:\arccos(e^{7x})
integral from 0 to 1 of (x^3)/(x^2-x-6)	\int\:_{0}^{1}\frac{x^{3}}{x^{2}-x-6}dx
inverse oflaplace 1/(s^2+40s+2000)	inverselaplace\:\frac{1}{s^{2}+40s+2000}
8t^2y^{''}-16y=11t^2-1	8t^{2}y^{\prime\:\prime\:}-16y=11t^{2}-1
derivative of sqrt(cot(3x))	derivative\:\sqrt{\cot(3x)}
tangent of f(x)=2x^3+3x^2-12x+6	tangent\:f(x)=2x^{3}+3x^{2}-12x+6
integral of (2x^3)/(\sqrt[3]{x^4-5)}	\int\:\frac{2x^{3}}{\sqrt[3]{x^{4}-5}}dx
maclaurin ln(1+x^3)	maclaurin\:\ln(1+x^{3})
integral of-5csc^2(x)+5	\int\:-5\csc^{2}(x)+5dx
integral of (xe^{-x})	\int\:(xe^{-x})dx
(\partial)/(\partial y)(xy(x-2)(y+3))	\frac{\partial\:}{\partial\:y}(xy(x-2)(y+3))
limit as x approaches 0 of x^2+sin^2(x)	\lim\:_{x\to\:0}(x^{2}+\sin^{2}(x))
(\partial)/(\partial y)(2arctan(x/y))	\frac{\partial\:}{\partial\:y}(2\arctan(\frac{x}{y}))
derivative of f(x)=(4x+5)^2	derivative\:f(x)=(4x+5)^{2}
integral of cos^5(x)tan^3(x)	\int\:\cos^{5}(x)\tan^{3}(x)dx
integral of 14sin^{-3/2}(x)cos^3(x)	\int\:14\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx
7x(dy)/(dx)=2xe^x-7y+6x^2	7x\frac{dy}{dx}=2xe^{x}-7y+6x^{2}
d/(dθ)(sin(θ)(4cos(θ)-4))	\frac{d}{dθ}(\sin(θ)(4\cos(θ)-4))
limit as x approaches 0 of ln^2(x)	\lim\:_{x\to\:0}(\ln^{2}(x))
integral from 0 to 5 of (x^3)/(x^4+4)	\int\:_{0}^{5}\frac{x^{3}}{x^{4}+4}dx
derivative of (x-8^2)	\frac{d}{dx}((x-8)^{2})
area 3x^2,sqrt(1/3 x),0,0.5	area\:3x^{2},\sqrt{\frac{1}{3}x},0,0.5
derivative of f(x)=(x^2-6x)/(x+1)	derivative\:f(x)=\frac{x^{2}-6x}{x+1}
derivative of 4sin(t)	derivative\:4\sin(t)
derivative of e^{3x+5}	\frac{d}{dx}(e^{3x+5})
integral of 2r(sin(θ))z^3	\int\:2r(\sin(θ))z^{3}
area x^2,x^3,0, 1/4	area\:x^{2},x^{3},0,\frac{1}{4}
sum from n=1 to infinity of 1/(n9^n)	\sum\:_{n=1}^{\infty\:}\frac{1}{n9^{n}}
limit as x approaches infinity of 0.5^x	\lim\:_{x\to\:\infty\:}(0.5^{x})
integral of (log_{4}(x))/x	\int\:\frac{\log_{4}(x)}{x}dx
limit as x approaches-2 of (2-x)^2	\lim\:_{x\to\:-2}((2-x)^{2})
derivative of arctan(ln(4x^5))	\frac{d}{dx}(\arctan(\ln(4)x^{5}))
limit as y approaches 6+of (y+6)/(y^2-36)	\lim\:_{y\to\:6+}(\frac{y+6}{y^{2}-36})
area y=10x,y=x^2-11,x	area\:y=10x,y=x^{2}-11,x
x^{''}+2x^'+2x=2	x^{\prime\:\prime\:}+2x^{\prime\:}+2x=2
derivative of-2ln(cos(x))	\frac{d}{dx}(-2\ln(\cos(x)))
integral of x*e^{2x^2}	\int\:x\cdot\:e^{2x^{2}}dx
derivative of y=sqrt(x/(x+5))	derivative\:y=\sqrt{\frac{x}{x+5}}
integral from 1 to 2 of-x^2+3x-2	\int\:_{1}^{2}-x^{2}+3x-2dx
2x^2(dy)/(dx)+2xy=y^3	2x^{2}\frac{dy}{dx}+2xy=y^{3}
integral of sqrt(36-9x^2)	\int\:\sqrt{36-9x^{2}}dx

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