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Popular Calculus Problems

integral from 1 to 5 of 4x^2ln(x)	\int\:_{1}^{5}4x^{2}\ln(x)dx
f^'(x)=2sin(6x),f(pi/6)=-5/2	f^{\prime\:}(x)=2\sin(6x),f(\frac{π}{6})=-\frac{5}{2}
limit as x approaches 1 of sin(5pix)	\lim\:_{x\to\:1}(\sin(5pix))
limit as x approaches 1+of (x^2+1)/(x-1)	\lim\:_{x\to\:1+}(\frac{x^{2}+1}{x-1})
(\partial)/(\partial x)(x^4+2x^2y^2)	\frac{\partial\:}{\partial\:x}(x^{4}+2x^{2}y^{2})
derivative of 8x^3+2x+7x^{1/3}	derivative\:8x^{3}+2x+7x^{\frac{1}{3}}
integral of e^x+xe^x	\int\:e^{x}+xe^{x}dx
derivative of (x^2-2xe^x)	\frac{d}{dx}((x^{2}-2x)e^{x})
integral of xsin(-3x)	\int\:x\sin(-3x)dx
integral of ln(x^2+1)	\int\:\ln(x^{2}+1)dx
laplacetransform e^{2t}sin(5t)	laplacetransform\:e^{2t}\sin(5t)
derivative of (4-3x-x^2)/(x^2-6)	derivative\:\frac{4-3x-x^{2}}{x^{2}-6}
integral from 0 to pi/2 of-2sin^2(3x)	\int\:_{0}^{\frac{π}{2}}-2\sin^{2}(3x)dx
((dy)/(dx))=0.011y(2-(y-25))	(\frac{dy}{dx})=0.011\cdot\:y\cdot\:(2-(y-25))
integral of 5/((3x-1)^7)	\int\:\frac{5}{(3x-1)^{7}}dx
(d^2)/(dx^2)(4xcos(x^2))	\frac{d^{2}}{dx^{2}}(4x\cos(x^{2}))
inverse oflaplace (4s)/(s^2+6s+9)	inverselaplace\:\frac{4s}{s^{2}+6s+9}
limit as x approaches 0 of (1+3x)^{7/x}	\lim\:_{x\to\:0}((1+3x)^{\frac{7}{x}})
laplacetransform 5sin(6t)	laplacetransform\:5\sin(6t)
integral of te^{-4t}	\int\:te^{-4t}dt
derivative of arctan(-x)	\frac{d}{dx}(\arctan(-x))
derivative of 8e^xcos(x)	derivative\:8e^{x}\cos(x)
sum from k=0 to infinity of (-3/4)^k	\sum\:_{k=0}^{\infty\:}(-\frac{3}{4})^{k}
derivative of-(x-1^2+3)	\frac{d}{dx}(-(x-1)^{2}+3)
derivative of (12x^6-3x^2+x^2/(3x^4))	\frac{d}{dx}(\frac{12x^{6}-3x^{2}+x^{2}}{3x^{4}})
integral of cos(x)*sin^2(x)	\int\:\cos(x)\cdot\:\sin^{2}(x)dx
integral of x^{5/3}	\int\:x^{\frac{5}{3}}dx
integral of sec^2(8x)	\int\:\sec^{2}(8x)dx
(y*e^{-x})(dy)/(dx)=x	(y\cdot\:e^{-x})\frac{dy}{dx}=x
integral from 0 to pi of sqrt(1+cos(2x))	\int\:_{0}^{π}\sqrt{1+\cos(2x)}dx
(\partial)/(\partial x)(x+y^2+xy+3)	\frac{\partial\:}{\partial\:x}(x+y^{2}+xy+3)
slope of y=x^3-3	slope\:y=x^{3}-3
sum from n=2 to infinity of \sqrt[n]{n}	\sum\:_{n=2}^{\infty\:}\sqrt[n]{n}
(\partial)/(\partial x)((x^2*y)/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}\cdot\:y}{x^{2}+y^{2}})
tan(θ)dr+2rdθ=0	\tan(θ)dr+2rdθ=0
derivative of sin(x)ln(6x)	derivative\:\sin(x)\ln(6x)
(\partial)/(\partial t)(2/((x-3t)^2+1))	\frac{\partial\:}{\partial\:t}(\frac{2}{(x-3t)^{2}+1})
(\partial)/(\partial x)(x^6y^8+7x^7y)	\frac{\partial\:}{\partial\:x}(x^{6}y^{8}+7x^{7}y)
integral of x^2sin(x^3+4)	\int\:x^{2}\sin(x^{3}+4)dx
limit as x approaches c of x	\lim\:_{x\to\:c}(x)
(\partial)/(\partial x)(xy^2-x^2y)	\frac{\partial\:}{\partial\:x}(xy^{2}-x^{2}y)
area y=4-x^2,y=-3x	area\:y=4-x^{2},y=-3x
integral from 1 to 2 of pi(1/x)^2	\int\:_{1}^{2}π(\frac{1}{x})^{2}dx
integral from 5 to 11 of (16)/(x-1)	\int\:_{5}^{11}\frac{16}{x-1}dx
integral from 0 to 1 of (x^2-x)^2	\int\:_{0}^{1}(x^{2}-x)^{2}dx
derivative of (tan(x)/x)	\frac{d}{dx}(\frac{\tan(x)}{x})
sum from n=0 to infinity of n/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{n}{3^{n}}
f(x)=arccos(2x)	f(x)=\arccos(2x)
limit as x approaches 0+of (e^{1/x})/x	\lim\:_{x\to\:0+}(\frac{e^{\frac{1}{x}}}{x})
derivative of (3x+4)^2	derivative\:(3x+4)^{2}
d/(dt)(2t-1)	\frac{d}{dt}(2t-1)
(\partial)/(\partial x)(-xe^{y/x})	\frac{\partial\:}{\partial\:x}(-xe^{\frac{y}{x}})
t^3(dy)/(dt)+3t^2y=9cos(t),y(pi)=0	t^{3}\frac{dy}{dt}+3t^{2}y=9\cos(t),y(π)=0
laplacetransform cos(10t)	laplacetransform\:\cos(10t)
(\partial)/(\partial x)(e^x(x-y)^2)	\frac{\partial\:}{\partial\:x}(e^{x}(x-y)^{2})
integral of (x-2)(2x+3)	\int\:(x-2)(2x+3)dx
x(dy)/(dx)=yln(xy)	x\frac{dy}{dx}=y\ln(xy)
(\partial)/(\partial x)(sin(y)e^x)	\frac{\partial\:}{\partial\:x}(\sin(y)e^{x})
sum from n=0 to infinity of (3^n)/n	\sum\:_{n=0}^{\infty\:}\frac{3^{n}}{n}
integral from 0 to 2 of-3x^3sqrt(x^2+4)	\int\:_{0}^{2}-3x^{3}\sqrt{x^{2}+4}dx
inverse oflaplace (16)/(s^2+3s+16)	inverselaplace\:\frac{16}{s^{2}+3s+16}
integral from 0 to 2 of x/(x^2+1)	\int\:_{0}^{2}\frac{x}{x^{2}+1}dx
(y/2+2x)dx+(-1)dy=0	(\frac{y}{2}+2x)dx+(-1)dy=0
area y=3,y=sqrt(x),x=0	area\:y=3,y=\sqrt{x},x=0
(xdy)/(dx)+xy=1-y	\frac{xdy}{dx}+xy=1-y
(dy)/(dx)=-2y	\frac{dy}{dx}=-2y
sum from n=2 to infinity of ne^{-3n}	\sum\:_{n=2}^{\infty\:}ne^{-3n}
limit as n approaches infinity of 2^{-n}	\lim\:_{n\to\:\infty\:}(2^{-n})
integral from 0 to-0.5 of 70x	\int\:_{0}^{-0.5}70xdx
(\partial)/(\partial x)(x*sin(y))	\frac{\partial\:}{\partial\:x}(x\cdot\:\sin(y))
(\partial)/(\partial x)(y-yx^2)	\frac{\partial\:}{\partial\:x}(y-yx^{2})
derivative of f(x)=(14x+4x^2)/((7+4x)^2)	derivative\:f(x)=\frac{14x+4x^{2}}{(7+4x)^{2}}
(\partial)/(\partial x)(-2kl(ln(y/(-x-y))))	\frac{\partial\:}{\partial\:x}(-2kl(\ln(\frac{y}{-x-y})))
integral of 1/(6-sqrt(x))	\int\:\frac{1}{6-\sqrt{x}}dx
derivative of g(x)=sqrt(2x-3)	derivative\:g(x)=\sqrt{2x-3}
integral of 14θsec^2(θ)	\int\:14θ\sec^{2}(θ)dθ
derivative of 9-x^2-y^2	\frac{d}{dx}(9-x^{2}-y^{2})
derivative of sqrt(3)(x^3-x^2)	derivative\:\sqrt{3}(x^{3}-x^{2})
integral of (3e^x)/(e^{2x)+6e^x+9}	\int\:\frac{3e^{x}}{e^{2x}+6e^{x}+9}dx
y^'+2y=16	y^{\prime\:}+2y=16
integral of x(x^2-1)^5	\int\:x(x^{2}-1)^{5}dx
(d^2)/(dx^2)(e^x-x^5)	\frac{d^{2}}{dx^{2}}(e^{x}-x^{5})
integral of sqrt(1+((x^2)/4-1/(x^2))^2)	\int\:\sqrt{1+(\frac{x^{2}}{4}-\frac{1}{x^{2}})^{2}}dx
y^{''}-4y^'=e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}=e^{2x}
derivative of (h/2)^2	derivative\:(\frac{h}{2})^{2}
integral from 0 to 4 of (64sqrt(x)-8x^2)	\int\:_{0}^{4}(64\sqrt{x}-8x^{2})dx
integral of (2x-8)/(sqrt(1-x-x^2))	\int\:\frac{2x-8}{\sqrt{1-x-x^{2}}}dx
(\partial)/(\partial y)(xln(xy-5))	\frac{\partial\:}{\partial\:y}(x\ln(xy-5))
integral from 0 to 9 of (1/3 x-2)	\int\:_{0}^{9}(\frac{1}{3}x-2)dx
(5+x)y^'-y=0	(5+x)y^{\prime\:}-y=0
integral of u-1	\int\:u-1du
integral of (tan(ln(4x+3)))/(4x+3)	\int\:\frac{\tan(\ln(4x+3))}{4x+3}dx
(\partial)/(\partial y)(tan(1+2x^2y^3z^2))	\frac{\partial\:}{\partial\:y}(\tan(1+2x^{2}y^{3}z^{2}))
(x+1/x)^'	(x+\frac{1}{x})^{\prime\:}
derivative of [x+(x+sin^2(x))^3]^5	derivative\:[x+(x+\sin^{2}(x))^{3}]^{5}
derivative of (ln(x+1)/(4x+2))	\frac{d}{dx}(\frac{\ln(x+1)}{4x+2})
integral of sec^3(4x)	\int\:\sec^{3}(4x)dx
derivative of 1 1/x	\frac{d}{dx}(1\frac{1}{x})
derivative of (3x+1^6sqrt(2x-5))	\frac{d}{dx}((3x+1)^{6}\sqrt{2x-5})
integral of 2sqrt(x)	\int\:2\sqrt{x}dx

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