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Popular Calculus Problems

integral from 0 to 3 of 1/(sqrt(3-x))	\int\:_{0}^{3}\frac{1}{\sqrt{3-x}}dx
integral of 1/(2sqrt(1-x^2))	\int\:\frac{1}{2\sqrt{1-x^{2}}}dx
y^{''}+4y^'+4y=2e^{-2t}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=2e^{-2t}
taylor sqrt(x-1),0	taylor\:\sqrt{x-1},0
limit as x approaches 0 of 2/(3+4^{1/0)}	\lim\:_{x\to\:0}(\frac{2}{3+4^{\frac{1}{0}}})
tangent of y=(16x)/(x^2+16),(-2,-8/5)	tangent\:y=\frac{16x}{x^{2}+16},(-2,-\frac{8}{5})
y^{''}-9y=0,y(0)=7	y^{\prime\:\prime\:}-9y=0,y(0)=7
integral of 3/((x+3)^2)	\int\:\frac{3}{(x+3)^{2}}dx
derivative of f(x)=3^{x^2-x+5}	derivative\:f(x)=3^{x^{2}-x+5}
(dy)/(dx)+7=e^{7x+y-5}	\frac{dy}{dx}+7=e^{7x+y-5}
integral of 5/(xsqrt(25-(ln(x))^2))	\int\:\frac{5}{x\sqrt{25-(\ln(x))^{2}}}dx
integral of cos(x)e^{-3x}	\int\:\cos(x)e^{-3x}dx
tangent of y= x/(sqrt(25+x^2)),(0,0)	tangent\:y=\frac{x}{\sqrt{25+x^{2}}},(0,0)
integral of (4e^{2t}i+3e^tj)	\int\:(4e^{2t}i+3e^{t}j)dt
(\partial)/(\partial x)(x/(x^2+2y^2)+3x)	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{2}+2y^{2}}+3x)
limit as x approaches 1 of 2\|x-1\|-1	\lim\:_{x\to\:1}(2\left\|x-1\right\|-1)
ay^{''}+by=0	ay^{\prime\:\prime\:}+by=0
derivative of sin((pix)/2)	derivative\:\sin(\frac{πx}{2})
derivative of 2sin(3x)	derivative\:2\sin(3x)
integral of (sin(1/(x^3)))/(x^4)	\int\:\frac{\sin(\frac{1}{x^{3}})}{x^{4}}dx
(\partial)/(\partial x)(((4x-4y))/(4x+4y))	\frac{\partial\:}{\partial\:x}(\frac{(4x-4y)}{4x+4y})
(\partial)/(\partial x)(tan(8+2x^2y^4z^2))	\frac{\partial\:}{\partial\:x}(\tan(8+2x^{2}y^{4}z^{2}))
(\partial)/(\partial x)(324x^2-324xy+81y^2)	\frac{\partial\:}{\partial\:x}(324x^{2}-324xy+81y^{2})
area 4cos(3x),4sin(6x),0, pi/6	area\:4\cos(3x),4\sin(6x),0,\frac{π}{6}
derivative of 8arcsin(x^4)	derivative\:8\arcsin(x^{4})
integral from 0.1 to 0.2 of 300x	\int\:_{0.1}^{0.2}300xdx
integral of sqrt(cos(x))	\int\:\sqrt{\cos(x)}dx
derivative of tan(2)x^2	derivative\:\tan(2)x^{2}
derivative of 5-x^{2/3}	\frac{d}{dx}(5-x^{\frac{2}{3}})
integral of y^2+ysin(x)	\int\:y^{2}+y\sin(x)
integral of (1-e^x)/(1+e^x)	\int\:\frac{1-e^{x}}{1+e^{x}}dx
f(x)=sqrt(x)sin(x)	f(x)=\sqrt{x}\sin(x)
y^'=e^{3x+2y}	y^{\prime\:}=e^{3x+2y}
taylor e^{2x-3}	taylor\:e^{2x-3}
(\partial)/(\partial x)(1/(3x^2+y))	\frac{\partial\:}{\partial\:x}(\frac{1}{3x^{2}+y})
limit as x approaches-3 of g(x)(f(x))	\lim\:_{x\to\:-3}(g(x)(f(x)))
integral of x(1-x)^{10}	\int\:x(1-x)^{10}dx
(\partial)/(\partial x)(y/(x^2-y^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{x^{2}-y^{2}})
derivative of 2xlog_{10}(sqrt(x))	\frac{d}{dx}(2x\log_{10}(\sqrt{x}))
t(dQ)/(dt)+Q=t^5ln(t)	t\frac{dQ}{dt}+Q=t^{5}\ln(t)
integral from 0 to \sqrt[3]{pi/2 of}21x^2sin^3(x^3)	\int\:_{0}^{\sqrt[3]{\frac{π}{2}}}21x^{2}\sin^{3}(x^{3})dx
integral of 3/(1+2e^x-e^{-x)}	\int\:\frac{3}{1+2e^{x}-e^{-x}}dx
limit as t approaches-1 of t^2-x^2	\lim\:_{t\to\:-1}(t^{2}-x^{2})
integral of ((xe^x))/((1+x)^2)	\int\:\frac{(xe^{x})}{(1+x)^{2}}dx
(\partial)/(\partial z)(z-x)	\frac{\partial\:}{\partial\:z}(z-x)
derivative of 1/(x^5+1/(x^6))	\frac{d}{dx}(\frac{1}{x^{5}}+\frac{1}{x^{6}})
integral of (x+1)sqrt(6-x)	\int\:(x+1)\sqrt{6-x}dx
derivative of (2+x^2)	\frac{d}{dx}((2+x)^{2})
integral from 1 to 2 of 2^{-θ}	\int\:_{1}^{2}2^{-θ}dθ
(d^2)/(dx^2)(x/(x^2-3))	\frac{d^{2}}{dx^{2}}(\frac{x}{x^{2}-3})
limit as x approaches-3-of sqrt(x^3+27)	\lim\:_{x\to\:-3-}(\sqrt{x^{3}+27})
integral of (a+b/(x-a))^2	\int\:(a+\frac{b}{x-a})^{2}dx
f(x)=((x+1)/(x-1))^2	f(x)=(\frac{x+1}{x-1})^{2}
f(x)= 1/(3x^2)	f(x)=\frac{1}{3x^{2}}
integral of 7sin^2(x)cos^2(x)	\int\:7\sin^{2}(x)\cos^{2}(x)dx
integral of (2sec^2(x)-5cos(x))	\int\:(2\sec^{2}(x)-5\cos(x))dx
taylor log_{10}(x+1)	taylor\:\log_{10}(x+1)
y^{''}+4y^'+4y=t-2e-2t	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=t-2e-2t
limit as x approaches 2 of 1/(x+2)	\lim\:_{x\to\:2}(\frac{1}{x+2})
integral of sin(x)-cos(x)+4	\int\:\sin(x)-\cos(x)+4dx
integral of (e^xsin(y)+tan(y))	\int\:(e^{x}\sin(y)+\tan(y))dx
(\partial)/(\partial y)(yln(y)+ye^x)	\frac{\partial\:}{\partial\:y}(y\ln(y)+ye^{x})
d/(dl)((dl^2-d-al^3-bl^2)/(l^2))	\frac{d}{dl}(\frac{dl^{2}-d-al^{3}-bl^{2}}{l^{2}})
integral of (sin(2x))/((1-cos^2(x))^3)	\int\:\frac{\sin(2x)}{(1-\cos^{2}(x))^{3}}dx
inverse oflaplace (-3)/((s+3)^2)	inverselaplace\:\frac{-3}{(s+3)^{2}}
derivative of 17e^x	derivative\:17e^{x}
(\partial)/(\partial t)(e^{-t})	\frac{\partial\:}{\partial\:t}(e^{-t})
integral of cos(3x)sin(x)	\int\:\cos(3x)\sin(x)dx
derivative of (9x^6+4x^3)^4	derivative\:(9x^{6}+4x^{3})^{4}
laplacetransform 8e^{(-2t)}tcos(3t)cos(t)	laplacetransform\:8\cdot\:e^{(-2t)}\cdot\:t\cdot\:\cos(3t)\cdot\:\cos(t)
(\partial)/(\partial z)((z^2+2x+y)/(xy))	\frac{\partial\:}{\partial\:z}(\frac{z^{2}+2x+y}{xy})
integral of p(p+9)^8	\int\:p(p+9)^{8}dp
integral of (2x-3)/x	\int\:\frac{2x-3}{x}dx
sqrt(x)+sqrt(y)(dy)/(dx)=0,y(16)=4	\sqrt{x}+\sqrt{y}\frac{dy}{dx}=0,y(16)=4
area x= 1/(y^2),x=1,x=4	area\:x=\frac{1}{y^{2}},x=1,x=4
integral of (-8)/(sqrt(x^2+16))	\int\:\frac{-8}{\sqrt{x^{2}+16}}dx
derivative of arctan(sin(7x))	\frac{d}{dx}(\arctan(\sin(7x)))
(dy)/(dx)+6y=xe^{-6x}	\frac{dy}{dx}+6y=xe^{-6x}
(\partial)/(\partial x)(48x^7y^7+30x^5y^5)	\frac{\partial\:}{\partial\:x}(48x^{7}y^{7}+30x^{5}y^{5})
derivative of-3sqrt(7x-1)	\frac{d}{dx}(-3\sqrt{7x-1})
integral of o	\int\:odo
f(t)=1+ln(t)	f(t)=1+\ln(t)
2yy^'+2=y^2+2x,y(0)=8	2yy^{\prime\:}+2=y^{2}+2x,y(0)=8
(\partial)/(\partial v)(3vsin(u))	\frac{\partial\:}{\partial\:v}(3v\sin(u))
integral of 1/(sqrt(2^2+x^2))	\int\:\frac{1}{\sqrt{2^{2}+x^{2}}}dx
integral of (x^2-4x+4)	\int\:(x^{2}-4x+4)dx
d/(dt)((2t-1)/(2t+1))	\frac{d}{dt}(\frac{2t-1}{2t+1})
inverse oflaplace 2/(s^5)	inverselaplace\:\frac{2}{s^{5}}
limit as x approaches 0 of sin(x^{12})	\lim\:_{x\to\:0}(\sin(x^{12}))
derivative of xarcsec(x^3)	\frac{d}{dx}(x\arcsec(x^{3}))
inverse oflaplace ((6+6s))/(2s^2+1)	inverselaplace\:\frac{(6+6s)}{2s^{2}+1}
limit as x approaches 1+of (x-3)/(x-1)	\lim\:_{x\to\:1+}(\frac{x-3}{x-1})
derivative of 9x^{1/2}	derivative\:9x^{\frac{1}{2}}
tangent of f(x)=x+1/x ,\at x=4	tangent\:f(x)=x+\frac{1}{x},\at\:x=4
derivative of 7x^6	\frac{d}{dx}(7x^{6})
limit as x approaches 0 of ((sin(3x)))/x	\lim\:_{x\to\:0}(\frac{(\sin(3x))}{x})
x^2y^{''}-5xy^'+9y=0	x^{2}y^{\prime\:\prime\:}-5xy^{\prime\:}+9y=0
limit as x approaches 2 of x^2-7x+5	\lim\:_{x\to\:2}(x^{2}-7x+5)
(\partial)/(\partial x)(1/(x^2+y^2+1))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}+y^{2}+1})
integral from 0 to 1 of xe^{-8x^2}	\int\:_{0}^{1}xe^{-8x^{2}}dx

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