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Popular Calculus Problems
integral from 0 to 4 of (sqrt(y)-y+2)
\int\:_{0}^{4}(\sqrt{y}-y+2)dy
limit as t approaches-2 of (t^2-4)/(t+2)
\lim\:_{t\to\:-2}(\frac{t^{2}-4}{t+2})
(\partial)/(\partial x)(7xe^{xy})
\frac{\partial\:}{\partial\:x}(7xe^{xy})
integral of sqrt((7+x)/(7-x))
\int\:\sqrt{\frac{7+x}{7-x}}dx
integral of sqrt((1-cos^2(x))^3)
\int\:\sqrt{(1-\cos^{2}(x))^{3}}dx
derivative of (e^{3x}-1)^5
derivative\:(e^{3x}-1)^{5}
(\partial)/(\partial x)(-(2x)/((x+y)^2))
\frac{\partial\:}{\partial\:x}(-\frac{2x}{(x+y)^{2}})
derivative of-3cos^{12}(x)
\frac{d}{dx}(-3\cos^{12}(x))
derivative of (x^2+1/(2x^2-3x))
\frac{d}{dx}(\frac{x^{2}+1}{2x^{2}-3x})
integral of x*cos(7x)
\int\:x\cdot\:\cos(7x)dx
f(x)=(\sqrt[5]{x^3})/(\sqrt[10]{x^4)}
f(x)=\frac{\sqrt[5]{x^{3}}}{\sqrt[10]{x^{4}}}
implicit (dy)/(dx),sqrt(x+y)+xy=21
implicit\:\frac{dy}{dx},\sqrt{x+y}+xy=21
integral of sqrt(a^2+x^2)
\int\:\sqrt{a^{2}+x^{2}}dx
integral of (1-sqrt(x+1))/(1+sqrt(x+1))
\int\:\frac{1-\sqrt{x+1}}{1+\sqrt{x+1}}dx
limit as x approaches 0 of x|x|
\lim\:_{x\to\:0}(x\left|x\right|)
inverse oflaplace (e^{-2s})/(s^2(s-1))
inverselaplace\:\frac{e^{-2s}}{s^{2}(s-1)}
(\partial)/(\partial x)(e^{-2x}*cos(2piy))
\frac{\partial\:}{\partial\:x}(e^{-2x}\cdot\:\cos(2πy))
derivative of (sec^2(x)dx)
\frac{d}{dx}((\sec^{2}(x))dx)
(dy)/(dx)+y=9
\frac{dy}{dx}+y=9
(\partial)/(\partial z)(x^4y+xz-yz^2-7)
\frac{\partial\:}{\partial\:z}(x^{4}y+xz-yz^{2}-7)
integral of x^y
\int\:x^{y}dx
derivative of cos(x-x*sin(x))
\frac{d}{dx}(\cos(x)-x\cdot\:\sin(x))
inverse oflaplace 1/(s+a)
inverselaplace\:\frac{1}{s+a}
tangent of x^3-3x^2+x-5
tangent\:x^{3}-3x^{2}+x-5
(\partial)/(\partial x)(x^3+ky^2-5xy)
\frac{\partial\:}{\partial\:x}(x^{3}+ky^{2}-5xy)
integral of 3xsqrt(1-x^2)
\int\:3x\sqrt{1-x^{2}}dx
4xy^'=2xe^x-4y+6x^2
4xy^{\prime\:}=2xe^{x}-4y+6x^{2}
integral of xsin^3(x^2)cos(x^2)
\int\:x\sin^{3}(x^{2})\cos(x^{2})dx
(dy)/(dx)=x,y(11)=5
\frac{dy}{dx}=x,y(11)=5
tangent of y=5sec(x),\at x= pi/3
tangent\:y=5\sec(x),\at\:x=\frac{π}{3}
derivative of-5e^{-4x}
\frac{d}{dx}(-5e^{-4x})
integral from 0 to 2 of (x+1)
\int\:_{0}^{2}(x+1)dx
derivative of y=1+2/(x^4)
derivative\:y=1+\frac{2}{x^{4}}
integral of y+y(3+y^2)^{1/2}
\int\:y+y(3+y^{2})^{\frac{1}{2}}dy
integral of x^3sqrt(100-x^2)
\int\:x^{3}\sqrt{100-x^{2}}dx
derivative of x^2cos(xy)
\frac{d}{dx}(x^{2}\cos(xy))
(4/(x^2))^'
(\frac{4}{x^{2}})^{\prime\:}
derivative of (3x^4-x^3(x^2+x^3))
\frac{d}{dx}((3x^{4}-x^{3})(x^{2}+x^{3}))
(\partial)/(\partial x)(xy^3+6)
\frac{\partial\:}{\partial\:x}(xy^{3}+6)
x^2y^'+y=0,y(8)=5
x^{2}y^{\prime\:}+y=0,y(8)=5
integral from 0 to 3 of 1/((x+2)(x+4))
\int\:_{0}^{3}\frac{1}{(x+2)(x+4)}dx
inverse oflaplace (10s)/(s^2-25)
inverselaplace\:\frac{10s}{s^{2}-25}
limit as x approaches-5 of-1x
\lim\:_{x\to\:-5}(-1x)
limit as x approaches 0 of 1/(x^2+3)
\lim\:_{x\to\:0}(\frac{1}{x^{2}+3})
integral of xe^2x
\int\:xe^{2}xdx
integral of (x^3+5)/(x^2)
\int\:\frac{x^{3}+5}{x^{2}}dx
tangent of (sqrt(x)+1)/(sqrt(x)+5)
tangent\:\frac{\sqrt{x}+1}{\sqrt{x}+5}
derivative of xe^x+x-5e^x-5
\frac{d}{dx}(xe^{x}+x-5e^{x}-5)
derivative of y=xsin(2/x)
derivative\:y=x\sin(\frac{2}{x})
integral of 4t+1
\int\:4t+1dt
derivative of (x+9)/(x^2-7x+1)
derivative\:\frac{x+9}{x^{2}-7x+1}
(\partial)/(\partial x)(7x^{5y})
\frac{\partial\:}{\partial\:x}(7x^{5y})
derivative of 8/(|x-2|^3)
\frac{d}{dx}(\frac{8}{\left|x-2\right|^{3}})
integral of (2x^2+2x-3)^{10}*(2x+1)
\int\:(2x^{2}+2x-3)^{10}\cdot\:(2x+1)dx
d/(d{x)}((sqrt(9-{x)^2-{y}^2})/({x)+{z}})
\frac{d}{d{x}}(\frac{\sqrt{9-{x}^{2}-{y}^{2}}}{{x}+{z}})
derivative of cos(7pix)
\frac{d}{dx}(\cos(7πx))
limit as x approaches 0 of (x^{-2}-6^{-2})/(x+6)
\lim\:_{x\to\:0}(\frac{x^{-2}-6^{-2}}{x+6})
area f(x)=2x+3,[-1,2]
area\:f(x)=2x+3,[-1,2]
integral of (sin(2u)-cos(3u))^2
\int\:(\sin(2u)-\cos(3u))^{2}du
derivative of (-2x)/((x^2-1)^2)
derivative\:\frac{-2x}{(x^{2}-1)^{2}}
(cos(3x))y^'-3(tan(3x))y=2(sec(3x))
(\cos(3x))y^{\prime\:}-3(\tan(3x))y=2(\sec(3x))
f(t)=4t
f(t)=4t
integral of sin^{1/2}(x)cos^3(x)
\int\:\sin^{\frac{1}{2}}(x)\cos^{3}(x)dx
limit as x approaches 0 of x/(ln(x))
\lim\:_{x\to\:0}(\frac{x}{\ln(x)})
y^'+2/x y=x
y^{\prime\:}+\frac{2}{x}y=x
(1-cos(x))^'
(1-\cos(x))^{\prime\:}
y^'-3y^2=0
y^{\prime\:}-3y^{2}=0
integral of 2x(4x+7)^8
\int\:2x(4x+7)^{8}dx
limit as x approaches infinity of x!
\lim\:_{x\to\:\infty\:}(x!)
integral from 1 to 2 of 6x^24^{x^3}
\int\:_{1}^{2}6x^{2}4^{x^{3}}dx
limit as x approaches 3 of (x-3)/(|x-3|)
\lim\:_{x\to\:3}(\frac{x-3}{\left|x-3\right|})
integral of (4x^2+2)/((x^2-2x+2)^2)
\int\:\frac{4x^{2}+2}{(x^{2}-2x+2)^{2}}dx
derivative of (2x^{(-3x)})
\frac{d}{dx}((2x)^{(-3x)})
tangent of y=7-x^2
tangent\:y=7-x^{2}
tangent of y=(1-x)(x^2-8)^2,(3,-2)
tangent\:y=(1-x)(x^{2}-8)^{2},(3,-2)
(dx)/(dt)=-x-x^2
\frac{dx}{dt}=-x-x^{2}
derivative of ln(3x+2)
derivative\:\ln(3x+2)
limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n
\lim\:_{n\to\:\infty\:}(\sum\:_{i=1}^{n}\frac{i^{3}}{n^{4}}+\frac{1}{n})
derivative of m(t)=5t(3t^4-1)^5
derivative\:m(t)=5t(3t^{4}-1)^{5}
derivative of xcos(y-ye^x)
\frac{d}{dx}(x\cos(y)-ye^{x})
derivative of f(x)=6x^5e^x+e^xx^6
derivative\:f(x)=6x^{5}e^{x}+e^{x}x^{6}
integral of tan(x)[ln(cos(x))]
\int\:\tan(x)[\ln(\cos(x))]dx
derivative of f(x)=cos(θ^2)
derivative\:f(x)=\cos(θ^{2})
limit as x approaches 5 of (x^2-7x+10)/(x^2-25)
\lim\:_{x\to\:5}(\frac{x^{2}-7x+10}{x^{2}-25})
(\partial)/(\partial x)(1/4 x^2+y^2)
\frac{\partial\:}{\partial\:x}(\frac{1}{4}x^{2}+y^{2})
tangent of y=1sqrt(x)
tangent\:y=1\sqrt{x}
integral from 3 to infinity of e^{-4x}
\int\:_{3}^{\infty\:}e^{-4x}dx
(dy)/(dx)=(2y+sqrt(x^2-y^2))/(2x)
\frac{dy}{dx}=\frac{2y+\sqrt{x^{2}-y^{2}}}{2x}
inverse oflaplace 3/(s+1)
inverselaplace\:\frac{3}{s+1}
integral of (sec^6(x))/(tan^3(x))
\int\:\frac{\sec^{6}(x)}{\tan^{3}(x)}dx
limit as x approaches 0-of e^{3/x}
\lim\:_{x\to\:0-}(e^{\frac{3}{x}})
(\partial)/(\partial x)(9)
\frac{\partial\:}{\partial\:x}(9)
derivative of [x+(x+sin^2(x)^3]^5)
\frac{d}{dx}([x+(x+\sin^{2}(x))^{3}]^{5})
integral from 0 to 1 of 2^{-x}
\int\:_{0}^{1}2^{-x}dx
derivative of (ln(x)/x)
\frac{d}{dx}(\frac{\ln(x)}{x})
(dy)/(dx)=(((2y+7))/(8x+9))^2
\frac{dy}{dx}=(\frac{(2y+7)}{8x+9})^{2}
integral from 0 to 2 of (6ti-t^3j+5t^9k)
\int\:_{0}^{2}(6ti-t^{3}j+5t^{9}k)dt
limit as x approaches 0 of (x+5)/(3x)
\lim\:_{x\to\:0}(\frac{x+5}{3x})
(\partial)/(\partial x)((e^{x/2})(2xy))
\frac{\partial\:}{\partial\:x}((e^{\frac{x}{2}})(2xy))
derivative of (x^2)/(x-9)
derivative\:\frac{x^{2}}{x-9}
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