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Popular Calculus Problems
integral of (sin(x))/(sec(x))
\int\:\frac{\sin(x)}{\sec(x)}dx
integral from 0 to 2 of 1/((x-2)^2)
\int\:_{0}^{2}\frac{1}{(x-2)^{2}}dx
integral of-y/((x+2)^2)
\int\:-\frac{y}{(x+2)^{2}}dx
tangent of f(x)=x^3+3x,\at x=2
tangent\:f(x)=x^{3}+3x,\at\:x=2
(\partial)/(\partial x)(x*cos(y))
\frac{\partial\:}{\partial\:x}(x\cdot\:\cos(y))
integral of \sqrt[3]{3x}
\int\:\sqrt[3]{3x}dx
limit as x approaches infinity of (x)^3
\lim\:_{x\to\:\infty\:}((x)^{3})
integral of (10x)/(sqrt(1-x^4))
\int\:\frac{10x}{\sqrt{1-x^{4}}}dx
limit as x approaches+0-of (sin(|x|))/x
\lim\:_{x\to\:+0-}(\frac{\sin(\left|x\right|)}{x})
derivative of 10^{2x-1}
\frac{d}{dx}(10^{2x-1})
integral of x/(sqrt(x^2)\sqrt{x^2-1)}
\int\:\frac{x}{\sqrt{x^{2}}\sqrt{x^{2}-1}}dx
(\partial)/(\partial x)(18ye^{9x})
\frac{\partial\:}{\partial\:x}(18ye^{9x})
integral of (x-9)sin(pix)
\int\:(x-9)\sin(πx)dx
((dy)/(dx))+6y=e^{-x}
(\frac{dy}{dx})+6y=e^{-x}
derivative of f(x)=5sin(x)
derivative\:f(x)=5\sin(x)
derivative of (x^2+5x/(x+2))
\frac{d}{dx}(\frac{x^{2}+5x}{x+2})
y^{''}-4y^'+y=0
y^{\prime\:\prime\:}-4y^{\prime\:}+y=0
integral of 1/(9+x^2)
\int\:\frac{1}{9+x^{2}}dx
integral from 0 to 2 of (2^x+6)
\int\:_{0}^{2}(2^{x}+6)dx
(\partial)/(\partial v)(asin(u)cos(v))
\frac{\partial\:}{\partial\:v}(a\sin(u)\cos(v))
derivative of |x-1|+|2x+3|
\frac{d}{dx}(\left|x-1\right|+\left|2x+3\right|)
area y=2x^2,y=8x-6x^2
area\:y=2x^{2},y=8x-6x^{2}
integral from 0 to 4pi of x^2sin(2x)
\int\:_{0}^{4π}x^{2}\sin(2x)dx
integral of 5-cos(x)
\int\:5-\cos(x)dx
derivative of \sqrt[6]{u}
derivative\:\sqrt[6]{u}
limit as x approaches pi/2 of sec^2(x)
\lim\:_{x\to\:\frac{π}{2}}(\sec^{2}(x))
(\partial)/(\partial x)(x/((x-1)^2))
\frac{\partial\:}{\partial\:x}(\frac{x}{(x-1)^{2}})
integral of sqrt(x)*sqrt(1+1/(4x))
\int\:\sqrt{x}\cdot\:\sqrt{1+\frac{1}{4x}}dx
y^{'''}+y^{''}=8x^2
y^{\prime\:\prime\:\prime\:}+y^{\prime\:\prime\:}=8x^{2}
integral of 2sin^2(x)cos^3(x)
\int\:2\sin^{2}(x)\cos^{3}(x)dx
integral of 1/(sqrt(a^2-u^2))
\int\:\frac{1}{\sqrt{a^{2}-u^{2}}}du
integral from 0 to x of sin((pit^2)/2)
\int\:_{0}^{x}\sin(\frac{πt^{2}}{2})dt
(\partial)/(\partial x)(e^{-x^2})
\frac{\partial\:}{\partial\:x}(e^{-x^{2}})
integral of (11sqrt(x)+sqrt(5))
\int\:(11\sqrt{x}+\sqrt{5})dx
integral of x^3sqrt(1+4x^2)
\int\:x^{3}\sqrt{1+4x^{2}}dx
implicit (dy)/(dx),y^6=x^5
implicit\:\frac{dy}{dx},y^{6}=x^{5}
derivative of sqrt(2-3x)
derivative\:\sqrt{2-3x}
integral of x*sin(nx)
\int\:x\cdot\:\sin(nx)dx
laplacetransform 5sin(100t)sin(5t)
laplacetransform\:5\sin(100t)\sin(5t)
derivative of ysin(2x)
\frac{d}{dx}(y\sin(2x))
derivative of-1/6 (x^{-6}-x^{12})
derivative\:-\frac{1}{6}(x^{-6}-x^{12})
integral from 0 to pi/7 of sin^4(7x)
\int\:_{0}^{\frac{π}{7}}\sin^{4}(7x)dx
integral of (1/8 x)x^2
\int\:(\frac{1}{8}x)x^{2}dx
derivative of arcsin(sqrt(sin(13x)))
\frac{d}{dx}(\arcsin(\sqrt{\sin(13x)}))
integral of arcsec(sqrt(t))
\int\:\arcsec(\sqrt{t})dt
derivative of 1/(sqrt(4-3x))
\frac{d}{dx}(\frac{1}{\sqrt{4-3x}})
simplify-x/y
simplify\:-\frac{x}{y}
integral of sin(x)sqrt(1+cos^2(x))
\int\:\sin(x)\sqrt{1+\cos^{2}(x)}dx
(dP)/(dt)=P(10^{-1}-P*10^{-7}),P(0)=7000
\frac{dP}{dt}=P(10^{-1}-P\cdot\:10^{-7}),P(0)=7000
derivative of f(x)=x^{-1/2}
derivative\:f(x)=x^{-\frac{1}{2}}
y^{''}-3y^'+4y=2,y(0)=0,y^'(0)=0
y^{\prime\:\prime\:}-3y^{\prime\:}+4y=2,y(0)=0,y^{\prime\:}(0)=0
(ds)/(dt)
\frac{ds}{dt}
integral from 1 to 2 of 2e^{-2x}
\int\:_{1}^{2}2e^{-2x}dx
(\partial)/(\partial x)(2x-4y)
\frac{\partial\:}{\partial\:x}(2x-4y)
derivative of h(x)=5sin^3(3+x)
derivative\:h(x)=5\sin^{3}(3+x)
limit as x approaches 2 of-x^2+6x-7
\lim\:_{x\to\:2}(-x^{2}+6x-7)
derivative of y(θ)=cos(θ)sin(θ)
derivative\:y(θ)=\cos(θ)\sin(θ)
integral of (sin(2x))/(38+cos^2(x))
\int\:\frac{\sin(2x)}{38+\cos^{2}(x)}dx
(\partial)/(\partial z)(9x^{y/z})
\frac{\partial\:}{\partial\:z}(9x^{\frac{y}{z}})
integral of x^2*e^{x^2}
\int\:x^{2}\cdot\:e^{x^{2}}dx
limit as x approaches 2 of 3^x+ln(x-1)
\lim\:_{x\to\:2}(3^{x}+\ln(x-1))
tangent of f(2)= 4/(1+x^2),\at x=1
tangent\:f(2)=\frac{4}{1+x^{2}},\at\:x=1
ty^'+2y=sin(t)
ty^{\prime\:}+2y=\sin(t)
integral of 6x(2x^2+9)^{1/2}
\int\:6x(2x^{2}+9)^{\frac{1}{2}}dx
integral of (cos(x)+sin(x))/(sin(2x))
\int\:\frac{\cos(x)+\sin(x)}{\sin(2x)}dx
f^'(x)=x^4+3x^3+5x^2+2x
f^{\prime\:}(x)=x^{4}+3x^{3}+5x^{2}+2x
derivative of 380000-1/32 x
\frac{d}{dx}(380000-\frac{1}{32}x)
integral of (3x+5)e^{3x+5}
\int\:(3x+5)e^{3x+5}dx
integral of cos(pinx)
\int\:\cos(πnx)dx
(dy)/(dx)=4cos(x)(3+2y)^2
\frac{dy}{dx}=4\cos(x)(3+2y)^{2}
integral from-2 to 3 of 2x
\int\:_{-2}^{3}2xdx
derivative of (x+1/(x-1))
\frac{d}{dx}(\frac{x+1}{x-1})
limit as x approaches 0 of cos(x)
\lim\:_{x\to\:0}(\cos(x))
integral of (sqrt(x^2-49))/(x^4)
\int\:\frac{\sqrt{x^{2}-49}}{x^{4}}dx
integral of 1/(x(1-x^2))
\int\:\frac{1}{x(1-x^{2})}dx
derivative of (60/(0.01x^2+1))
\frac{d}{dx}(\frac{60}{0.01x^{2}+1})
derivative of-9/(sqrt(x))
\frac{d}{dx}(-\frac{9}{\sqrt{x}})
(arctan(1/x))^'
(\arctan(\frac{1}{x}))^{\prime\:}
(\partial)/(\partial x)(x^{4cos(x)})
\frac{\partial\:}{\partial\:x}(x^{4\cos(x)})
integral of (4+x^2)/(x^3)
\int\:\frac{4+x^{2}}{x^{3}}dx
(dQ)/(dt)=3-(3Q)/(1000)
\frac{dQ}{dt}=3-\frac{3Q}{1000}
derivative of f(x)=4^{sin^2(x)+cos(3x)}
derivative\:f(x)=4^{\sin^{2}(x)+\cos(3x)}
limit as x approaches-1 of sqrt(|x|-x)
\lim\:_{x\to\:-1}(\sqrt{\left|x\right|-x})
derivative of y=pix
derivative\:y=πx
(2x+5)y^'+10y=10(2x+5)
(2x+5)y^{\prime\:}+10y=10(2x+5)
sum from n=0 to infinity of 3/(5^n)
\sum\:_{n=0}^{\infty\:}\frac{3}{5^{n}}
derivative of (x^2/(sqrt(x^2+9)))
\frac{d}{dx}(\frac{x^{2}}{\sqrt{x^{2}+9}})
integral of (x^2-2x)
\int\:(x^{2}-2x)dx
integral of x^{11}e^{-x^6}
\int\:x^{11}e^{-x^{6}}dx
integral of sec^2(3x+1)
\int\:\sec^{2}(3x+1)dx
integral of 1/(y(4-y))
\int\:\frac{1}{y(4-y)}dy
derivative of 7(e^xcos(x-e^xsin(x)))
\frac{d}{dx}(7(e^{x}\cos(x)-e^{x}\sin(x)))
derivative of \sqrt[3]{(x^2-1)^2}
derivative\:\sqrt[3]{(x^{2}-1)^{2}}
(dy)/(dx)=(3x)/(5y)
\frac{dy}{dx}=\frac{3x}{5y}
derivative of sqrt(x^2+4)
derivative\:\sqrt{x^{2}+4}
(\partial)/(\partial x)(y^{xz}+2(yz)^x)
\frac{\partial\:}{\partial\:x}(y^{xz}+2(yz)^{x})
integral of 2\sqrt[4]{x}
\int\:2\sqrt[4]{x}dx
integral of (tan(ln(y)))/y
\int\:\frac{\tan(\ln(y))}{y}dy
integral of 120x(2x+120)^4
\int\:120x(2x+120)^{4}dx
2x(dy)/(dx)=10x^3y^5+y
2x\frac{dy}{dx}=10x^{3}y^{5}+y
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