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Popular Calculus Problems

integral of 1/(sqrt(289+x^2))	\int\:\frac{1}{\sqrt{289+x^{2}}}dx
integral from 0 to 1 of (x^{15}+15^x)	\int\:_{0}^{1}(x^{15}+15^{x})dx
x^2y^{''}-xy^'+y=x	x^{2}y^{\prime\:\prime\:}-xy^{\prime\:}+y=x
limit as x approaches 9-of x^2-3x	\lim\:_{x\to\:9-}(x^{2}-3x)
integral of ((ln(x))^{7/2})/x	\int\:\frac{(\ln(x))^{\frac{7}{2}}}{x}dx
integral from-infinity to 2 of e^x	\int\:_{-\infty\:}^{2}e^{x}dx
limit as x approaches 2 of x^3+x^2+x	\lim\:_{x\to\:2}(x^{3}+x^{2}+x)
limit as x approaches 0 of (sin(7x))/(tan(11x))	\lim\:_{x\to\:0}(\frac{\sin(7x)}{\tan(11x)})
integral of x^2e^{19x}	\int\:x^{2}e^{19x}dx
derivative of (x-3/(x^2-5))	\frac{d}{dx}(\frac{x-3}{x^{2}-5})
integral of x^3*e^{x^4+5}	\int\:x^{3}\cdot\:e^{x^{4}+5}dx
derivative of (x+(2x)^{1/2})(2x+1)	derivative\:(x+(2x)^{\frac{1}{2}})(2x+1)
integral from 0 to pi/2 of sec^2(x)	\int\:_{0}^{\frac{π}{2}}\sec^{2}(x)dx
integral of (x^3+27)/(x+3)	\int\:\frac{x^{3}+27}{x+3}dx
integral of f	\int\:fdf
derivative of \sqrt[4]{2x-3y}	\frac{d}{dx}(\sqrt[4]{2x-3y})
integral from pi/4 to pi of sin(x)	\int\:_{\frac{π}{4}}^{π}\sin(x)dx
derivative of cos^4(x+sec(x^3))	\frac{d}{dx}(\cos^{4}(x)+\sec(x^{3}))
integral of cos(x)	\int\:\cos(x)dx
integral of 1/(sqrt(x^2+z^2))	\int\:\frac{1}{\sqrt{x^{2}+z^{2}}}dx
f(x)=4x+1	f(x)=4x+1
(dy)/(dt)-(3/t)y=2t^3e^{2t}	\frac{dy}{dt}-(\frac{3}{t})y=2t^{3}e^{2t}
(\partial)/(\partial x)(cos(5x-2y^2))	\frac{\partial\:}{\partial\:x}(\cos(5x-2y^{2}))
tangent of x^2+8	tangent\:x^{2}+8
sum from n=1 to infinity of 1/(4n^6+n+1)	\sum\:_{n=1}^{\infty\:}\frac{1}{4n^{6}+n+1}
(dy}{dx}=\frac{9x)/y	\frac{dy}{dx}=\frac{9x}{y}
integral of (1/(x*ln(x)))	\int\:(\frac{1}{x\cdot\:\ln(x)})dx
integral of 1/(sqrt(x^2-4x+5))	\int\:\frac{1}{\sqrt{x^{2}-4x+5}}dx
x^2y^'+2xy=15cos^2(x)	x^{2}y^{\prime\:}+2xy=15\cos^{2}(x)
integral from-1 to 2 of \|x^2-2x\|	\int\:_{-1}^{2}\left\|x^{2}-2x\right\|dx
derivative of f(x)=sqrt(4-x)	derivative\:f(x)=\sqrt{4-x}
limit as x approaches 0+of x^{3sin(x)}	\lim\:_{x\to\:0+}(x^{3\sin(x)})
integral of (1/4)^{x+1}	\int\:(\frac{1}{4})^{x+1}dx
integral of (x^2)/((x-1)^2)	\int\:\frac{x^{2}}{(x-1)^{2}}dx
integral of (x/(1+x^2))^2	\int\:(\frac{x}{1+x^{2}})^{2}dx
integral of 1/(x^a)	\int\:\frac{1}{x^{a}}dx
limit as x approaches-1+of x/(x+1)	\lim\:_{x\to\:-1+}(\frac{x}{x+1})
(\partial)/(\partial t)(sqrt(3t))	\frac{\partial\:}{\partial\:t}(\sqrt{3t})
(dy)/(dx)=(x+y-2)/(2x+2y+3)	\frac{dy}{dx}=\frac{x+y-2}{2x+2y+3}
integral of 1/(x^2-25)	\int\:\frac{1}{x^{2}-25}dx
(\partial)/(\partial x)(cos(x^8+y^8))	\frac{\partial\:}{\partial\:x}(\cos(x^{8}+y^{8}))
derivative of 5sqrt(x)+8	\frac{d}{dx}(5\sqrt{x}+8)
derivative of 1/(A^2sqrt(A))	derivative\:\frac{1}{A^{2}\sqrt{A}}
(\partial)/(\partial x)(4xln(y)+yln(z)-x)	\frac{\partial\:}{\partial\:x}(4x\ln(y)+y\ln(z)-x)
limit as x approaches 0 of (1-ln(x))^x	\lim\:_{x\to\:0}((1-\ln(x))^{x})
derivative of cot(2x^2-1)	\frac{d}{dx}(\cot(2x^{2}-1))
integral of 1/3 e^{x+3}	\int\:\frac{1}{3}e^{x+3}dx
tangent of sqrt(5x+1),\at x=3	tangent\:\sqrt{5x+1},\at\:x=3
derivative of-(3x^2sin((x^3/4))/(4))	\frac{d}{dx}(-\frac{3x^{2}\sin(\frac{x^{3}}{4})}{4})
tangent of 6sec(x),\at x= pi/6	tangent\:6\sec(x),\at\:x=\frac{π}{6}
derivative of (x+1/(x^2+x+1))	\frac{d}{dx}(\frac{x+1}{x^{2}+x+1})
limit as x approaches-2 of f(x)x	\lim\:_{x\to\:-2}(f(x)x)
derivative of cos(x(x^2+1)+(sqrt(3))/2)	\frac{d}{dx}(\cos(x(x^{2}+1))+\frac{\sqrt{3}}{2})
limit as x approaches 0 of xln(x+x^2)	\lim\:_{x\to\:0}(x\ln(x+x^{2}))
integral of (sqrt(x^2-64))/x	\int\:\frac{\sqrt{x^{2}-64}}{x}dx
derivative of (1+2x)/(3-4x)	derivative\:\frac{1+2x}{3-4x}
(\partial}{\partial x}(\frac{V(I,x))/I)	\frac{\partial\:}{\partial\:x}(\frac{V(I,x)}{I})
integral of e^{3x+2y}	\int\:e^{3x+2y}
integral of tan^2(x)sin(x)	\int\:\tan^{2}(x)\sin(x)dx
derivative of f(x)=7x^4	derivative\:f(x)=7x^{4}
(\partial)/(\partial x)((4xy)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{4xy}{x^{2}+y^{2}})
xy^'=y+(x+1)^2	xy^{\prime\:}=y+(x+1)^{2}
integral of (x^5+x^3)^{11}(5x^4+3x^2)	\int\:(x^{5}+x^{3})^{11}(5x^{4}+3x^{2})dx
inverse oflaplace ((s-1))/(s^2(s^2+2))	inverselaplace\:\frac{(s-1)}{s^{2}(s^{2}+2)}
integral of sec^5(x/2)	\int\:\sec^{5}(\frac{x}{2})dx
derivative of ln(tan(7x))	\frac{d}{dx}(\ln(\tan(7x)))
derivative of f(x)=(x^7+5x)^{1/3}	derivative\:f(x)=(x^{7}+5x)^{\frac{1}{3}}
integral of x/(x^2+16)	\int\:\frac{x}{x^{2}+16}dx
laplacetransform e^{3x}sin(6x)	laplacetransform\:e^{3x}\sin(6x)
integral of x/(x-21)	\int\:\frac{x}{x-21}dx
derivative of (x+2^2(x-1))	\frac{d}{dx}((x+2)^{2}(x-1))
integral from 0 to 1 of x^2+1	\int\:_{0}^{1}x^{2}+1dx
inverse oflaplace 1/(s((s-1)^2+1))	inverselaplace\:\frac{1}{s((s-1)^{2}+1)}
d/(dy)((y^2)/4)	\frac{d}{dy}(\frac{y^{2}}{4})
(d^2)/(dx^2)(xe^{-3x})	\frac{d^{2}}{dx^{2}}(xe^{-3x})
integral from 0 to 2pi of 2x^2sin(1/4 x)	\int\:_{0}^{2π}2x^{2}\sin(\frac{1}{4}x)dx
limit as x approaches 0 of 1/x*ln(x+1)	\lim\:_{x\to\:0}(\frac{1}{x}\cdot\:\ln(x+1))
integral of 6xyz+e^x	\int\:6xyz+e^{x}dy
(\partial)/(\partial y)(4x+8y-88)	\frac{\partial\:}{\partial\:y}(4x+8y-88)
limit as x approaches 0+of (x)ln(x^4)	\lim\:_{x\to\:0+}((x)\ln(x^{4}))
inverse oflaplace (40)/(1+25p+100p^2)	inverselaplace\:\frac{40}{1+25p+100p^{2}}
(\partial)/(\partial x)(xyz-sin(x+y+z))	\frac{\partial\:}{\partial\:x}(xyz-\sin(x+y+z))
integral of 8cot^4(x)	\int\:8\cot^{4}(x)dx
derivative of x^{3/2}-1	\frac{d}{dx}(x^{\frac{3}{2}}-1)
derivative of 4asec(xtan(x))	\frac{d}{dx}(4a\sec(x)\tan(x))
integral of (-x)/(1+x^4)	\int\:\frac{-x}{1+x^{4}}dx
y^'+y=2e^x,y(0)=20	y^{\prime\:}+y=2e^{x},y(0)=20
(\partial)/(\partial x)(3x^y)	\frac{\partial\:}{\partial\:x}(3x^{y})
integral of e^{-x}sin(-x)	\int\:e^{-x}\sin(-x)dx
(dx)/(x+1)=(xy+x-y-1)dy	\frac{dx}{x+1}=(xy+x-y-1)dy
(\partial)/(\partial x)(sin(ct)sin(x))	\frac{\partial\:}{\partial\:x}(\sin(ct)\sin(x))
integral from-3 to-5 of (-4)^{-3}	\int\:_{-3}^{-5}(-4)^{-3}dx
(x+xy^2)dx+(e^{x^2}y)dy=0	(x+xy^{2})dx+(e^{x^{2}}y)dy=0
integral of (10x^2-19x+6)/(x^3-3x^2+2x)	\int\:\frac{10x^{2}-19x+6}{x^{3}-3x^{2}+2x}dx
integral of tan^2(x)*sec^2(x)	\int\:\tan^{2}(x)\cdot\:\sec^{2}(x)dx
derivative of (x^3+3e^x)	\frac{d}{dx}((x^{3}+3)e^{x})
(\partial)/(\partial x)(Ax+By+Ce^{xy})	\frac{\partial\:}{\partial\:x}(Ax+By+Ce^{xy})
integral from 0 to 5 of 1/(x^{5/2)}	\int\:_{0}^{5}\frac{1}{x^{\frac{5}{2}}}dx
integral of 3x^2-4x+1	\int\:3x^{2}-4x+1dx
derivative of f(x)=(x^2+x+1)^3	derivative\:f(x)=(x^{2}+x+1)^{3}

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