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Popular Calculus Problems

integral from 1 to 5 of w^2ln(w)	\int\:_{1}^{5}w^{2}\ln(w)dw
integral of ({y})/(L{y\)}	\int\:\frac{\left\{y\right\}}{L\left\{y\right\}}dL
tangent of 5/((x^2+1))	tangent\:\frac{5}{(x^{2}+1)}
integral of 1+cos(2θ)	\int\:1+\cos(2θ)dθ
integral of (x^2-x-4)/(x^3+2x)	\int\:\frac{x^{2}-x-4}{x^{3}+2x}dx
integral of (x^3)/(sqrt((x+1)^2+4))	\int\:\frac{x^{3}}{\sqrt{(x+1)^{2}+4}}dx
derivative of 16^4sqrt(4x^4+4)	derivative\:16^{4}\sqrt{4x^{4}+4}
6y^'=x^2	6y^{\prime\:}=x^{2}
derivative of 1/3 x^3-x^2-8x+1	\frac{d}{dx}(\frac{1}{3}x^{3}-x^{2}-8x+1)
y^'=(2x^4+y^4)/(xy^3)	y^{\prime\:}=\frac{2x^{4}+y^{4}}{xy^{3}}
2x(dy)/(dx)=y^2	2x\frac{dy}{dx}=y^{2}
y^'=sqrt(9x+y)-9	y^{\prime\:}=\sqrt{9x+y}-9
integral of x/(x-6)	\int\:\frac{x}{x-6}dx
(\partial)/(\partial x)(2y-sin(x))	\frac{\partial\:}{\partial\:x}(2y-\sin(x))
derivative of 2/5 x^{15}	\frac{d}{dx}(\frac{2}{5}x^{15})
laplacetransform t^2cos(2t+30)	laplacetransform\:t^{2}\cos(2t+30^{\circ\:})
derivative of f(x)=5xsin(pix)	derivative\:f(x)=5x\sin(πx)
y^{''}-2y^'+y=e^xtan^{-1}(x)	y^{\prime\:\prime\:}-2y^{\prime\:}+y=e^{x}\tan^{-1}(x)
limit as x approaches-2 of [f(x)+g(x)]	\lim\:_{x\to\:-2}([f(x)+g(x)])
laplacetransform-5	laplacetransform\:-5
integral from 0 to 2pi of cos^3(θ)	\int\:_{0}^{2π}\cos^{3}(θ)dθ
derivative of (3x^2-4x+5/(6sqrt(x)))	\frac{d}{dx}(\frac{3x^{2}-4x+5}{6\sqrt{x}})
x(dy)/(dx)+y=9xy^2	x\frac{dy}{dx}+y=9xy^{2}
limit as x approaches 2+of 1/((x-2)^2)	\lim\:_{x\to\:2+}(\frac{1}{(x-2)^{2}})
(\partial)/(\partial x)(x/(x^2+81))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+81})
y^'-2y=3x^2	y^{\prime\:}-2y=3x^{2}
limit as x approaches 4 of x^2-16	\lim\:_{x\to\:4}(x^{2}-16)
limit as x approaches-2 of (5x+3)/(2x-9)	\lim\:_{x\to\:-2}(\frac{5x+3}{2x-9})
derivative of (2x^5-3)^8	derivative\:(2x^{5}-3)^{8}
integral from 0 to 2 of ((x+2))/((x-4))	\int\:_{0}^{2}\frac{(x+2)}{(x-4)}dx
(\partial)/(\partial x)(36-6x^2-y^2)	\frac{\partial\:}{\partial\:x}(36-6x^{2}-y^{2})
taylor (2x)/(sqrt(e^{2x^2)-1)}	taylor\:\frac{2x}{\sqrt{e^{2x^{2}}-1}}
derivative of 2sqrt(3)sin(x+2cos(x))	\frac{d}{dx}(2\sqrt{3}\sin(x)+2\cos(x))
integral from 1 to 2 of 3	\int\:_{1}^{2}3dx
slope of (x^2+y^2)^2=4x^2y,(-1,1)	slope\:(x^{2}+y^{2})^{2}=4x^{2}y,(-1,1)
limit as x approaches 0 of (x+2)/x	\lim\:_{x\to\:0}(\frac{x+2}{x})
derivative of 5/(x+10)	\frac{d}{dx}(\frac{5}{x+10})
derivative of f(x)=e^{9sqrt(x)}	derivative\:f(x)=e^{9\sqrt{x}}
derivative of e^{-x}*cos(x)	\frac{d}{dx}(e^{-x}\cdot\:\cos(x))
inverse oflaplace 1/(s^2+s+2)	inverselaplace\:\frac{1}{s^{2}+s+2}
sum from n=0 to infinity of ((7-8n))/(4+3n)	\sum\:_{n=0}^{\infty\:}\frac{(7-8n)}{4+3n}
integral of-6/(x^2)	\int\:-\frac{6}{x^{2}}dx
tangent of sqrt(5x+1),\at x=7	tangent\:\sqrt{5x+1},\at\:x=7
derivative of (x/(x+1)^x)	\frac{d}{dx}((\frac{x}{x+1})^{x})
integral from 4 to 9 of (sqrt(x))	\int\:_{4}^{9}(\sqrt{x})dx
integral of 1/(sqrt(8-4x-4x^2))	\int\:\frac{1}{\sqrt{8-4x-4x^{2}}}dx
y^'+2y=3e^t	y^{\prime\:}+2y=3e^{t}
integral from 0 to 2 of x/(x^2+4)	\int\:_{0}^{2}\frac{x}{x^{2}+4}dx
limit as x approaches-3-of 1/(x^2-9)	\lim\:_{x\to\:-3-}(\frac{1}{x^{2}-9})
integral of 1/(4sqrt(x)(6+\sqrt{x))}	\int\:\frac{1}{4\sqrt{x}(6+\sqrt{x})}dx
derivative of (2000t)/(4t+75)	derivative\:\frac{2000t}{4t+75}
(\partial)/(\partial x)(sqrt(x+2))	\frac{\partial\:}{\partial\:x}(\sqrt{x+2})
integral of (15e^{5z})/(e^{5z)+2}	\int\:\frac{15e^{5z}}{e^{5z}+2}dz
(\partial)/(\partial t)(x^2ycos(z/t))	\frac{\partial\:}{\partial\:t}(x^{2}y\cos(\frac{z}{t}))
derivative of f(x)=-(13)/(x^6)	derivative\:f(x)=-\frac{13}{x^{6}}
integral of 3/(tsqrt(t^2-1))	\int\:\frac{3}{t\sqrt{t^{2}-1}}dt
limit as x approaches+0 of x/(x-1)	\lim\:_{x\to\:+0}(\frac{x}{x-1})
derivative of f(x)=log_{10}(x^8+9)	derivative\:f(x)=\log_{10}(x^{8}+9)
derivative of e^{sin(x)}	derivative\:e^{\sin(x)}
d/(dy)((y^3-8)/(y^3+8))	\frac{d}{dy}(\frac{y^{3}-8}{y^{3}+8})
integral of e^x(x^2+2x)	\int\:e^{x}(x^{2}+2x)dx
(\partial)/(\partial x)(xc^2(1/(sqrt(1-\frac{v^2){c^2)}}-1))	\frac{\partial\:}{\partial\:x}(xc^{2}(\frac{1}{\sqrt{1-\frac{v^{2}}{c^{2}}}}-1))
integral from 0 to 1 of t/((2-t)^2)	\int\:_{0}^{1}\frac{t}{(2-t)^{2}}dt
integral of 1/(xsqrt(144x^2-144))	\int\:\frac{1}{x\sqrt{144x^{2}-144}}dx
tangent of f(x)= 2/(x-4),\at x=6	tangent\:f(x)=\frac{2}{x-4},\at\:x=6
integral of (6x^6+3x^5+5x-4)	\int\:(6x^{6}+3x^{5}+5x-4)dx
(\partial)/(\partial x)(e^{ix}cos(iy))	\frac{\partial\:}{\partial\:x}(e^{ix}\cos(iy))
integral of ln(x)*1/x	\int\:\ln(x)\cdot\:\frac{1}{x}dx
integral of (sqrt(1-x^2)-x)x	\int\:(\sqrt{1-x^{2}}-x)xdx
integral of (x^4+x-16)/(x^2+4)	\int\:\frac{x^{4}+x-16}{x^{2}+4}dx
derivative of ln(sqrt((a^2-z^2)/(a^2+z^2)))	derivative\:\ln(\sqrt{\frac{a^{2}-z^{2}}{a^{2}+z^{2}}})
derivative of y=3(4x^2+4)	derivative\:y=3(4x^{2}+4)
(\partial)/(\partial x)(zsqrt(x+y))	\frac{\partial\:}{\partial\:x}(z\sqrt{x+y})
(\partial)/(\partial x)(sqrt((x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\sqrt{(x^{2}+y^{2})})
derivative of (x^2-7x+13/(x-3))	\frac{d}{dx}(\frac{x^{2}-7x+13}{x-3})
y^{''}-2y^'=4t	y^{\prime\:\prime\:}-2y^{\prime\:}=4t
derivative of x/(10)	\frac{d}{dx}(\frac{x}{10})
limit as x approaches 10+of (x^3)/(x-10)	\lim\:_{x\to\:10+}(\frac{x^{3}}{x-10})
integral of 1/(x(1+2ln(x)))	\int\:\frac{1}{x(1+2\ln(x))}dx
limit as x approaches 0 of 2+3e^{1/x}	\lim\:_{x\to\:0}(2+3e^{\frac{1}{x}})
(\partial)/(\partial m)(m/v)	\frac{\partial\:}{\partial\:m}(\frac{m}{v})
d/(d{x)}(3({x}^2)i+5({y}^3)j+{z}k)	\frac{d}{d{x}}(3({x}^{2})i+5({y}^{3})j+{z}k)
limit as x approaches-5+of 3[x]+4	\lim\:_{x\to\:-5+}(3[x]+4)
(\partial)/(\partial z)(5ze^{xyz})	\frac{\partial\:}{\partial\:z}(5ze^{xyz})
integral of csc(a)ycot(a)y	\int\:\csc(a)y\cot(a)ydy
integral of 4/(x(x+2))	\int\:\frac{4}{x(x+2)}dx
integral from 0 to 4 of 1/(16+x^2)	\int\:_{0}^{4}\frac{1}{16+x^{2}}dx
inverse oflaplace 1/(2s^2+2)	inverselaplace\:\frac{1}{2s^{2}+2}
integral of (x+1)/(x+3)	\int\:\frac{x+1}{x+3}dx
(\partial)/(\partial y)(e^x*sin(y))	\frac{\partial\:}{\partial\:y}(e^{x}\cdot\:\sin(y))
integral of sin(t)1+cos(t)	\int\:\sin(t)1+\cos(t)dt
tangent of f(x)=(sqrt(x))/(x+5),\at x=4	tangent\:f(x)=\frac{\sqrt{x}}{x+5},\at\:x=4
slope of (3,5),(-1,5)	slope\:(3,5),(-1,5)
integral from 0 to 4 of xsqrt(x)	\int\:_{0}^{4}x\sqrt{x}dx
derivative of 4e^xsin(x)	\frac{d}{dx}(4e^{x}\sin(x))
derivative of 2-sqrt(y-x^2)	\frac{d}{dx}(2-\sqrt{y-x^{2}})
integral of x^2*ln(2x)	\int\:x^{2}\cdot\:\ln(2x)dx
limit as x approaches 2 of (\sqrt[3]{x}-2)/(x-8)	\lim\:_{x\to\:2}(\frac{\sqrt[3]{x}-2}{x-8})
integral from 0 to 1 of 1/(x^{19/18)}	\int\:_{0}^{1}\frac{1}{x^{\frac{19}{18}}}dx
derivative of e^{x^2}+x^2	\frac{d}{dx}(e^{x^{2}}+x^{2})

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