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Popular Calculus Problems

integral of (e^x+9)/(e^{2x)-6e^x+9}	\int\:\frac{e^{x}+9}{e^{2x}-6e^{x}+9}dx
f(x)=e^{7x}	f(x)=e^{7x}
d/(dθ)(sqrt(l^2-(lsin(θ)-x(θ))^2)-lcos(θ))	\frac{d}{dθ}(\sqrt{l^{2}-(l\sin(θ)-x(θ))^{2}}-l\cos(θ))
(dy)/(dx)=(4x)/(3y)	\frac{dy}{dx}=\frac{4x}{3y}
limit as x approaches 0 of 3/(x^2)	\lim\:_{x\to\:0}(\frac{3}{x^{2}})
limit as x approaches 3 of 2x^2	\lim\:_{x\to\:3}(2x^{2})
limit as x approaches 3 of 2x^2+5x-2	\lim\:_{x\to\:3}(2x^{2}+5x-2)
derivative of (x+1)^x	derivative\:(x+1)^{x}
derivative of sqrt(x^5+2)	\frac{d}{dx}(\sqrt{x^{5}+2})
integral from 0 to 8 of (3+x)	\int\:_{0}^{8}(3+x)dx
(dy)/(dx)-y=2x-3	\frac{dy}{dx}-y=2x-3
integral of (-2)/y	\int\:\frac{-2}{y}dy
d/(du)(sqrt(u/v))	\frac{d}{du}(\sqrt{\frac{u}{v}})
f(x)=1+sin^2(x)	f(x)=1+\sin^{2}(x)
integral of sec(t)(6sec(t)+7tan(t))	\int\:\sec(t)(6\sec(t)+7\tan(t))dt
derivative of 7/(x^2+1)	\frac{d}{dx}(\frac{7}{x^{2}+1})
integral of x^3sqrt(x^2+32)	\int\:x^{3}\sqrt{x^{2}+32}dx
derivative of 3cos(x+2sin(x))	\frac{d}{dx}(3\cos(x)+2\sin(x))
derivative of (x+1/(x^{2/3)(x+3)^{1/3}})	\frac{d}{dx}(\frac{x+1}{x^{\frac{2}{3}}(x+3)^{\frac{1}{3}}})
integral of e^{kx}	\int\:e^{kx}dx
integral of sqrt(t)-1/(sqrt(t))	\int\:\sqrt{t}-\frac{1}{\sqrt{t}}dt
slope of (1,5),(-2,-4)	slope\:(1,5),(-2,-4)
xy^'+y=8xy^2,y(1)=5	xy^{\prime\:}+y=8xy^{2},y(1)=5
integral from 0 to pi/2 of 9sin^2(2x)	\int\:_{0}^{\frac{π}{2}}9\sin^{2}(2x)dx
(dy)/(dx)=-((2xy+y^2+1))/(x^2+2xy)	\frac{dy}{dx}=-\frac{(2xy+y^{2}+1)}{x^{2}+2xy}
derivative of (1x^3)/(2x^4)	derivative\:\frac{1x^{3}}{2x^{4}}
derivative of-2e^{-3x}	\frac{d}{dx}(-2e^{-3x})
(\partial)/(\partial x)(3xy^2-7)	\frac{\partial\:}{\partial\:x}(3xy^{2}-7)
integral of 2/3 sec^2(pix)	\int\:\frac{2}{3}\sec^{2}(πx)dx
integral of (cos(x)-1)/x	\int\:\frac{\cos(x)-1}{x}dx
slope of (8.6)(3.6)	slope\:(8.6)(3.6)
integral of (csc(ln(v^2)))/v	\int\:\frac{\csc(\ln(v^{2}))}{v}dv
derivative of 1x	derivative\:1x
derivative of f(x)=4sin(x)	derivative\:f(x)=4\sin(x)
6xy^'+5y=20	6xy^{\prime\:}+5y=20
derivative of (6x^2+4x+8/(sqrt(x)))	\frac{d}{dx}(\frac{6x^{2}+4x+8}{\sqrt{x}})
integral of (1-x)^2	\int\:(1-x)^{2}dx
integral of xsin(5-x)	\int\:x\sin(5-x)dx
inverse oflaplace 8/s	inverselaplace\:\frac{8}{s}
y^{''}+y^'-20y=-1200t^3	y^{\prime\:\prime\:}+y^{\prime\:}-20y=-1200t^{3}
(\partial)/(\partial x)((x+y)(xy+1))	\frac{\partial\:}{\partial\:x}((x+y)(xy+1))
integral of sqrt(x^2+6x+11)	\int\:\sqrt{x^{2}+6x+11}dx
integral of sin^2(x)sin(3x)	\int\:\sin^{2}(x)\sin(3x)dx
(\partial)/(\partial x)(sqrt(x+4))	\frac{\partial\:}{\partial\:x}(\sqrt{x+4})
inverse oflaplace 1/(2s^3+6s^2+4s)	inverselaplace\:\frac{1}{2s^{3}+6s^{2}+4s}
integral of x(sqrt(x))	\int\:x(\sqrt{x})dx
derivative of y=(3x+4)^5+15x(3x+4)^4	derivative\:y=(3x+4)^{5}+15x(3x+4)^{4}
integral of-e^{4x}	\int\:-e^{4x}dx
sum from n=1 to infinity of n/(csc(1/n))	\sum\:_{n=1}^{\infty\:}\frac{n}{\csc(\frac{1}{n})}
integral of ((arctan(x))^4)/(1+x^2)	\int\:\frac{(\arctan(x))^{4}}{1+x^{2}}dx
(\partial)/(\partial x)(yln(x^3+y^4+2))	\frac{\partial\:}{\partial\:x}(y\ln(x^{3}+y^{4}+2))
derivative of e^{x{z}(x})	\frac{d}{dx}(e^{x{z}(x)})
tangent of f(x)=x^2+169x+820,\at x=2	tangent\:f(x)=x^{2}+169x+820,\at\:x=2
derivative of y=(2x)/(7-cot(x))	derivative\:y=\frac{2x}{7-\cot(x)}
integral of (x^{-1/2})	\int\:(x^{-\frac{1}{2}})dx
integral from 1 to 9 of (sqrt(x))	\int\:_{1}^{9}(\sqrt{x})dx
integral of 49	\int\:49dx
(\partial)/(\partial x)(4y^2x^3-3yx^2)	\frac{\partial\:}{\partial\:x}(4y^{2}x^{3}-3yx^{2})
x^{''}+4x^'+2x=0	x^{\prime\:\prime\:}+4x^{\prime\:}+2x=0
integral of (5e^{-0.8x})	\int\:(5e^{-0.8x})dx
derivative of y=2xe^{2x}-e^{2x}	derivative\:y=2xe^{2x}-e^{2x}
(x-8y)dx+(4x)dy=0	(x-8y)dx+(4x)dy=0
inverse oflaplace ((s+1)^3)/(s^5)	inverselaplace\:\frac{(s+1)^{3}}{s^{5}}
limit as x approaches 5 of ((x-5))/(sqrt(x^2+5))	\lim\:_{x\to\:5}(\frac{(x-5)}{\sqrt{x^{2}+5}})
integral from 0 to infinity of 4sin^2(a)	\int\:_{0}^{\infty\:}4\sin^{2}(a)da
integral of 9t^6	\int\:9t^{6}dt
laplacetransform 5sin(3t)	laplacetransform\:5\sin(3t)
derivative of e^{x^6}	derivative\:e^{x^{6}}
integral of (4+sqrt(x)+x)/x	\int\:\frac{4+\sqrt{x}+x}{x}dx
(\partial)/(\partial y)(2xy^2+y)	\frac{\partial\:}{\partial\:y}(2xy^{2}+y)
derivative of f(x)=(x/(x^2+1))^2	derivative\:f(x)=(\frac{x}{x^{2}+1})^{2}
(dy)/(dx)+y=xe^{-x}+1	\frac{dy}{dx}+y=xe^{-x}+1
sum from n=0 to infinity of 1/(n(n+2))	\sum\:_{n=0}^{\infty\:}\frac{1}{n(n+2)}
limit as x approaches 5 of x^2-25	\lim\:_{x\to\:5}(x^{2}-25)
derivative of x(x^2+1^2)	\frac{d}{dx}(x(x^{2}+1)^{2})
integral from 0 to 1 of (4x+6)/((x+1)^2)	\int\:_{0}^{1}\frac{4x+6}{(x+1)^{2}}dx
derivative of-x^3+2x^2-x	\frac{d}{dx}(-x^{3}+2x^{2}-x)
integral of (3x^2-2)/(x^3-2x-8)	\int\:\frac{3x^{2}-2}{x^{3}-2x-8}dx
limit as x approaches-pi/4 of csc(x)	\lim\:_{x\to\:-\frac{π}{4}}(\csc(x))
sum from n=1 to infinity of ((1+n)/n)^n	\sum\:_{n=1}^{\infty\:}(\frac{1+n}{n})^{n}
derivative of (-1)/(sqrt(10+4t^2))	derivative\:\frac{-1}{\sqrt{10+4t^{2}}}
derivative of e^{x+y}sin(x-y)	\frac{d}{dx}(e^{x+y}\sin(x-y))
derivative of (x-2)(x-3)^2	derivative\:(x-2)(x-3)^{2}
integral of-(2ln(x))/(x^2)	\int\:-\frac{2\ln(x)}{x^{2}}dx
derivative of ln((x^2/((x-4))))	\frac{d}{dx}(\ln(\frac{x^{2}}{(x-4)}))
derivative of x^3e^{x^2}	\frac{d}{dx}(x^{3}e^{x^{2}})
derivative of f(x)=(3x-2)^4	derivative\:f(x)=(3x-2)^{4}
integral of cos(2x)-1	\int\:\cos(2x)-1dx
(dy)/(dx)=((x-y))/((x+2y))	\frac{dy}{dx}=\frac{(x-y)}{(x+2y)}
(\partial)/(\partial x)(sqrt(x^2+z^2))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{2}+z^{2}})
derivative of (3x^2+2x/(4x-3))	\frac{d}{dx}(\frac{3x^{2}+2x}{4x-3})
derivative of g(x)=3e^xsqrt(x)	derivative\:g(x)=3e^{x}\sqrt{x}
derivative of cos(x+xcos(y)-y)	\frac{d}{dx}(\cos(x)+x\cos(y)-y)
(\partial)/(\partial x)(xyz+9x+8y-4z)	\frac{\partial\:}{\partial\:x}(xyz+9x+8y-4z)
laplacetransform f(t)=1	laplacetransform\:f(t)=1
inverse oflaplace s/((s+1)^5)	inverselaplace\:\frac{s}{(s+1)^{5}}
integral of sin^3(3x)cos^5(3x)	\int\:\sin^{3}(3x)\cos^{5}(3x)dx
integral from-2 to 14 of 1/((x+2)^{1/4)}	\int\:_{-2}^{14}\frac{1}{(x+2)^{\frac{1}{4}}}dx
integral of (x^3)/(sqrt(x))	\int\:\frac{x^{3}}{\sqrt{x}}dx
integral of x+2-x^2	\int\:x+2-x^{2}dx

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