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Popular Calculus Problems

x^2y^{''}-3xy^'+4y=x^{5/2}	x^{2}y^{\prime\:\prime\:}-3xy^{\prime\:}+4y=x^{\frac{5}{2}}
(\partial)/(\partial x)(7ln((3xy)/(7z)))	\frac{\partial\:}{\partial\:x}(7\ln(\frac{3xy}{7z}))
integral of (sin^2(x))/(1-cos(x))	\int\:\frac{\sin^{2}(x)}{1-\cos(x)}dx
derivative of arcsin(9x^5)	\frac{d}{dx}(\arcsin(9x^{5}))
derivative of (8e^x)/(9e^x+5)	derivative\:\frac{8e^{x}}{9e^{x}+5}
integral of e^xsin(yz)	\int\:e^{x}\sin(yz)dx
integral of (x-1)/(x^2-2x+4)	\int\:\frac{x-1}{x^{2}-2x+4}dx
(dy)/(dx)=(9x)/(10y)	\frac{dy}{dx}=\frac{9x}{10y}
(\partial}{\partial x}(\frac{V(x))/x)	\frac{\partial\:}{\partial\:x}(\frac{V(x)}{x})
integral of x/((x-2)(x^2-4x+5)^2)	\int\:\frac{x}{(x-2)(x^{2}-4x+5)^{2}}dx
limit as x approaches 2 of x^5-8-2	\lim\:_{x\to\:2}(x^{5}-8-2)
derivative of x^{-3}+x^{-5}-2x^{-6}	\frac{d}{dx}(x^{-3}+x^{-5}-2x^{-6})
integral of 5cot^3(x)	\int\:5\cot^{3}(x)dx
integral from 1 to 3 of 3x^4ln(x)	\int\:_{1}^{3}3x^{4}\ln(x)dx
integral from 1 to 3 of 1/(x-2)	\int\:_{1}^{3}\frac{1}{x-2}dx
area x,0, 9/x ,x=5	area\:x,0,\frac{9}{x},x=5
derivative of 23arctan(sqrt(x))	\frac{d}{dx}(23\arctan(\sqrt{x}))
integral of (17xe^{2x})/((1+2x)^2)	\int\:\frac{17xe^{2x}}{(1+2x)^{2}}dx
integral of cos^6(θ)sin(θ)	\int\:\cos^{6}(θ)\sin(θ)dθ
(\partial)/(\partial y)(y^3sin(2x))	\frac{\partial\:}{\partial\:y}(y^{3}\sin(2x))
(dy)/(dx)=4	\frac{dy}{dx}=4
derivative of 4x^{3/5}	\frac{d}{dx}(4x^{\frac{3}{5}})
integral from 1 to 2 of (-12x+6)	\int\:_{1}^{2}(-12x+6)dx
y^'=(x^2-y^2)/(xy),y(2)=3	y^{\prime\:}=\frac{x^{2}-y^{2}}{xy},y(2)=3
integral of sin(3x)cos(4x)	\int\:\sin(3x)\cos(4x)dx
derivative of 3/(\sqrt[4]{x)}	derivative\:\frac{3}{\sqrt[4]{x}}
integral of ((x^2+1))/((x-6)(x-5)^2)	\int\:\frac{(x^{2}+1)}{(x-6)(x-5)^{2}}dx
integral of sqrt(7x+4)	\int\:\sqrt{7x+4}dx
(\partial)/(\partial x)(3xy^6+sin(pix)-z)	\frac{\partial\:}{\partial\:x}(3xy^{6}+\sin(πx)-z)
integral of x(6x^2-x+7)	\int\:x(6x^{2}-x+7)dx
area x,x^3-3x^2+3x,-0,1	area\:x,x^{3}-3x^{2}+3x,-0,1
tangent of (-5x)/(sqrt(2x-1))	tangent\:\frac{-5x}{\sqrt{2x-1}}
derivative of e^{bx}	derivative\:e^{bx}
integral from 0 to x of 1/(x^2)	\int\:_{0}^{x}\frac{1}{x^{2}}dx
derivative of sin^4(3x)	\frac{d}{dx}(\sin^{4}(3x))
integral of r^2((r^3)/(24)-6)^7	\int\:r^{2}(\frac{r^{3}}{24}-6)^{7}dr
laplacetransform sin(t+2)	laplacetransform\:\sin(t+2)
tangent of f(x)= 6/(x-1),(3,3)	tangent\:f(x)=\frac{6}{x-1},(3,3)
tangent of y=6x^2-7x+4,(1,3)	tangent\:y=6x^{2}-7x+4,(1,3)
derivative of sin(3x)cos(2x)	derivative\:\sin(3x)\cos(2x)
integral of sin^4(2x)cos^2(2x)	\int\:\sin^{4}(2x)\cos^{2}(2x)dx
integral of 3sin(5x)	\int\:3\sin(5x)dx
integral of 1/(1+x^{3/2)}	\int\:\frac{1}{1+x^{\frac{3}{2}}}dx
d/(dt)((tan(t))/(cos(t)-4))	\frac{d}{dt}(\frac{\tan(t)}{\cos(t)-4})
integral of (ln(11x))/x	\int\:\frac{\ln(11x)}{x}dx
integral of (x^3)^2	\int\:(x^{3})^{2}dx
derivative of f(x)=(x^3+8)/x	derivative\:f(x)=\frac{x^{3}+8}{x}
integral of sqrt(4+4x^2+x^4)	\int\:\sqrt{4+4x^{2}+x^{4}}dx
inverse oflaplace 6/((s^2*(s^2+8s+1)))	inverselaplace\:\frac{6}{(s^{2}\cdot\:(s^{2}+8s+1))}
derivative of sqrt(e^{2x)-16}	\frac{d}{dx}(\sqrt{e^{2x}-16})
derivative of 5sqrt(x)+6	\frac{d}{dx}(5\sqrt{x}+6)
integral of 7csc^2(x)	\int\:7\csc^{2}(x)dx
integral of r^2(r^3+6)^8	\int\:r^{2}(r^{3}+6)^{8}dr
(x+1)(x-2)y^'+y=0	(x+1)(x-2)y^{\prime\:}+y=0
(dy)/(dx)-1/x y=xy^2	\frac{dy}{dx}-\frac{1}{x}y=xy^{2}
integral of (3-2x)^{10}	\int\:(3-2x)^{10}dx
integral from 1 to 2 of (x^2+4)/(3x-x^2)	\int\:_{1}^{2}\frac{x^{2}+4}{3x-x^{2}}dx
(\partial)/(\partial y)(y/(y-x))	\frac{\partial\:}{\partial\:y}(\frac{y}{y-x})
integral of 147cos^2(x)	\int\:147\cos^{2}(x)dx
integral of (2x-5)^{10}	\int\:(2x-5)^{10}dx
integral of ln(x+1)	\int\:\ln(x+1)dx
inverse oflaplace ((12+4x))/(x-1)	inverselaplace\:\frac{(12+4x)}{x-1}
sum from n=0 to infinity of n(2/7)^n	\sum\:_{n=0}^{\infty\:}n(\frac{2}{7})^{n}
(\partial)/(\partial x)((x^3+y^2)^5)	\frac{\partial\:}{\partial\:x}((x^{3}+y^{2})^{5})
integral from 0 to pi/2 of 20cos^5(x)	\int\:_{0}^{\frac{π}{2}}20\cos^{5}(x)dx
integral from 1 to 2 of (6/(x^3)+2x)	\int\:_{1}^{2}(\frac{6}{x^{3}}+2x)dx
limit as x approaches 2 of x^3-x^2+2x	\lim\:_{x\to\:2}(x^{3}-x^{2}+2x)
inverse oflaplace 1/(2s^2+10s+12)	inverselaplace\:\frac{1}{2s^{2}+10s+12}
integral of x^{1/3}	\int\:x^{\frac{1}{3}}dx
derivative of ln(1+e^{-x})	\frac{d}{dx}(\ln(1+e^{-x}))
integral of (5x)/(1+x^4)	\int\:\frac{5x}{1+x^{4}}dx
derivative of 2x^3-3x^2-12x+5	\frac{d}{dx}(2x^{3}-3x^{2}-12x+5)
derivative of (x^2+4x/(x+2))	\frac{d}{dx}(\frac{x^{2}+4x}{x+2})
derivative of (-x^2+64/((x^2+64)^2))	\frac{d}{dx}(\frac{-x^{2}+64}{(x^{2}+64)^{2}})
derivative of f(x)=cos(x)+xsin(x)	derivative\:f(x)=\cos(x)+x\sin(x)
(\partial)/(\partial x)(4x+9y)	\frac{\partial\:}{\partial\:x}(4x+9y)
(\partial)/(\partial x)(x^4+5xy^9)	\frac{\partial\:}{\partial\:x}(x^{4}+5xy^{9})
limit as t approaches 0 of t^2	\lim\:_{t\to\:0}(t^{2})
(\partial)/(\partial y)(xln(x+2y))	\frac{\partial\:}{\partial\:y}(x\ln(x+2y))
d/(dt)((t+sin(t-1))^3(t^2-2)^5)	\frac{d}{dt}((t+\sin(t-1))^{3}(t^{2}-2)^{5})
integral of x*ln(x^2+1)	\int\:x\cdot\:\ln(x^{2}+1)dx
integral from 0 to 1 of ln(2x+1)	\int\:_{0}^{1}\ln(2x+1)dx
tangent of f(x)=-4x^2-3+2,\at x=-1	tangent\:f(x)=-4x^{2}-3+2,\at\:x=-1
integral from 0 to 1 of (x+1)/(x^2+1)	\int\:_{0}^{1}\frac{x+1}{x^{2}+1}dx
integral of (e^{1/(x^8)})/(x^9)	\int\:\frac{e^{\frac{1}{x^{8}}}}{x^{9}}dx
limit as x approaches-3 of (x-3)/(9x)	\lim\:_{x\to\:-3}(\frac{x-3}{9x})
(\partial)/(\partial x)(x^2+5xz+3yz^2)	\frac{\partial\:}{\partial\:x}(x^{2}+5xz+3yz^{2})
derivative of f(x)=8ln(t^8)	derivative\:f(x)=8\ln(t^{8})
derivative of y=(cos(x))/(x^5)	derivative\:y=\frac{\cos(x)}{x^{5}}
derivative of 1+e^{2x}	derivative\:1+e^{2x}
limit as x approaches 0+of (x^2)/7-7/x	\lim\:_{x\to\:0+}(\frac{x^{2}}{7}-\frac{7}{x})
limit as x approaches 0 of (9^x-15^x)/x	\lim\:_{x\to\:0}(\frac{9^{x}-15^{x}}{x})
derivative of (sin(x)/(2-cos(x)))	\frac{d}{dx}(\frac{\sin(x)}{2-\cos(x)})
integral of ((x-1)/(x^2))	\int\:(\frac{x-1}{x^{2}})dx
y^{''}-8y^'+17=0	y^{\prime\:\prime\:}-8y^{\prime\:}+17=0
derivative of U(x)=-0.04x^2+240x-10000	derivative\:U(x)=-0.04x^{2}+240x-10000
integral from 0 to 3 of e^x-x^2	\int\:_{0}^{3}e^{x}-x^{2}dx
(\partial)/(\partial x)(yln(x^3+y^4+3)-9)	\frac{\partial\:}{\partial\:x}(y\ln(x^{3}+y^{4}+3)-9)
limit as x approaches 2 of x^2-x+2	\lim\:_{x\to\:2}(x^{2}-x+2)
y^'=t-ty	y^{\prime\:}=t-ty

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