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Popular Calculus Problems

limit as x approaches-2 of-x^2-4x	\lim\:_{x\to\:-2}(-x^{2}-4x)
limit as x approaches 0-of x^2+1/x	\lim\:_{x\to\:0-}(x^{2}+\frac{1}{x})
maclaurin 2/(1-x^2)	maclaurin\:\frac{2}{1-x^{2}}
integral of 1/(4e^{-6x)+e^{6x}}	\int\:\frac{1}{4e^{-6x}+e^{6x}}dx
limit as x approaches 2 of 5x+3	\lim\:_{x\to\:2}(5x+3)
(dy)/(dx)=x	\frac{dy}{dx}=x
(\partial)/(\partial y)(e^x+cos(y))	\frac{\partial\:}{\partial\:y}(e^{x}+\cos(y))
integral of 1/(xln(x)-x)	\int\:\frac{1}{x\ln(x)-x}dx
(\partial)/(\partial x)(xe^y-e^z)	\frac{\partial\:}{\partial\:x}(xe^{y}-e^{z})
implicit (dy)/(dx),ye^x=y	implicit\:\frac{dy}{dx},ye^{x}=y
derivative of (3x+1((x^2+4))/((6x-5)))	\frac{d}{dx}((3x+1)\frac{(x^{2}+4)}{(6x-5)})
integral of (sin(2x))/(sin(x))	\int\:\frac{\sin(2x)}{\sin(x)}dx
(\partial)/(\partial x)((1-ln(x))/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{1-\ln(x)}{x^{2}})
(\partial)/(\partial x)(ln(9x))	\frac{\partial\:}{\partial\:x}(\ln(9x))
tangent of y=x^2+9x,\at x=-8	tangent\:y=x^{2}+9x,\at\:x=-8
derivative of-cos(e^x)	\frac{d}{dx}(-\cos(e^{x}))
integral from 1 to 6 of 1/(2sqrt(x+3)+x)	\int\:_{1}^{6}\frac{1}{2\sqrt{x+3}+x}dx
derivative of 7sqrt(x)(x^3-8sqrt(x)+2)	\frac{d}{dx}(7\sqrt{x}(x^{3}-8\sqrt{x}+2))
x(dy)/(dx)-2y=5x^3	x\frac{dy}{dx}-2y=5x^{3}
(\partial)/(\partial x)((x^2)/(sin^2(x)))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}}{\sin^{2}(x)})
(\partial)/(\partial z)(((x+y))/(y+z))	\frac{\partial\:}{\partial\:z}(\frac{(x+y)}{y+z})
limit as x approaches 2+of-5/(x-2)	\lim\:_{x\to\:2+}(-\frac{5}{x-2})
integral from 4 to-4 of (-7)	\int\:_{4}^{-4}(-7)dx
laplacetransform t^2+e^{-t}sin(2t)	laplacetransform\:t^{2}+e^{-t}\sin(2t)
integral of-e^{-3x}	\int\:-e^{-3x}dx
integral of (e^{2x})/x	\int\:\frac{e^{2x}}{x}dx
integral of (3-x^2)*2^x	\int\:(3-x^{2})\cdot\:2^{x}dx
y^{''}+7y^'+12y=0,y(0)=a,y^'(0)=b	y^{\prime\:\prime\:}+7y^{\prime\:}+12y=0,y(0)=a,y^{\prime\:}(0)=b
integral from-1 to 2 of x^4	\int\:_{-1}^{2}x^{4}dx
limit as n approaches infinity of Dn	\lim\:_{n\to\:\infty\:}(Dn)
integral of cos^6(x)tan^3(x)	\int\:\cos^{6}(x)\tan^{3}(x)dx
(\partial)/(\partial x)(sec(x)tan(y))	\frac{\partial\:}{\partial\:x}(\sec(x)\tan(y))
2y^'+1/x y=x^2y^{-1}	2y^{\prime\:}+\frac{1}{x}y=x^{2}y^{-1}
limit as x approaches 0 of ((2^x-7^x))/x	\lim\:_{x\to\:0}(\frac{(2^{x}-7^{x})}{x})
inverse oflaplace 1/(s(s^2+2s+5))	inverselaplace\:\frac{1}{s(s^{2}+2s+5)}
(dy)/(dx)=e^{x-y}	\frac{dy}{dx}=e^{x-y}
tangent of f(x)=x^3ln(2x),\at x=1	tangent\:f(x)=x^{3}\ln(2x),\at\:x=1
integral from 1 to 9 of sqrt(y)ln(y)	\int\:_{1}^{9}\sqrt{y}\ln(y)dy
(\partial)/(\partial x)(x/(sin(2x+3y+z^2)))	\frac{\partial\:}{\partial\:x}(\frac{x}{\sin(2x+3y+z^{2})})
(\partial)/(\partial u)(3vcos(u))	\frac{\partial\:}{\partial\:u}(3v\cos(u))
derivative of ln((x^2+4^5))	\frac{d}{dx}(\ln((x^{2}+4)^{5}))
limit as x approaches 4 of ((2))/(x-4)	\lim\:_{x\to\:4}(\frac{(2)}{x-4})
limit as x approaches 2-of (2x)/(x^2-4)	\lim\:_{x\to\:2-}(\frac{2x}{x^{2}-4})
y^{''}+8y^'+25y=0,y(0)=3,y^'(0)=-10	y^{\prime\:\prime\:}+8y^{\prime\:}+25y=0,y(0)=3,y^{\prime\:}(0)=-10
limit as x approaches-2+of (-7x)/(x+2)	\lim\:_{x\to\:-2+}(\frac{-7x}{x+2})
tangent of f(x)=4x^2+9x	tangent\:f(x)=4x^{2}+9x
f(x)=5x^3	f(x)=5x^{3}
(1+x)dy=(y+x)dx	(1+x)dy=(y+x)dx
tangent of f(x)=x^2-x+2,\at x=1	tangent\:f(x)=x^{2}-x+2,\at\:x=1
integral from-pi to 0 of 0	\int\:_{-π}^{0}0dx
integral from 0 to 4 of 1/((9-3x)^{1/3)}	\int\:_{0}^{4}\frac{1}{(9-3x)^{\frac{1}{3}}}dx
integral of 3x^2+C	\int\:3x^{2}+Cdx
derivative of f(x)=3x+5/x	derivative\:f(x)=3x+\frac{5}{x}
limit as x approaches 3+of xsqrt(x-3)	\lim\:_{x\to\:3+}(x\sqrt{x-3})
xy^'+3y=(4e^{-3x})/(x^2)	xy^{\prime\:}+3y=\frac{4e^{-3x}}{x^{2}}
derivative of sqrt(x^2+4x)	\frac{d}{dx}(\sqrt{x^{2}+4x})
(dy}{dx}=\frac{2x(y+1))/y	\frac{dy}{dx}=\frac{2x(y+1)}{y}
derivative of 48	\frac{d}{dx}(48)
derivative of 2/(sqrt(4x+3))	\frac{d}{dx}(\frac{2}{\sqrt{4x+3}})
y^'+(x+3)y^2=0	y^{\prime\:}+(x+3)y^{2}=0
derivative of 7x^{1/3}-7x^{-2/3}	derivative\:7x^{\frac{1}{3}}-7x^{-\frac{2}{3}}
integral of (x^2+2x-3)/(x^4)	\int\:\frac{x^{2}+2x-3}{x^{4}}dx
integral from 0 to y of 2e^{-x-y}	\int\:_{0}^{y}2e^{-x-y}dx
integral of cos(wt)	\int\:\cos(wt)dt
limit as x approaches-5 of (3x^2+15x)/(2x^2-50)	\lim\:_{x\to\:-5}(\frac{3x^{2}+15x}{2x^{2}-50})
derivative of y=(arctan(9x))^2	derivative\:y=(\arctan(9x))^{2}
integral of 3y^3	\int\:3y^{3}dy
limit as x approaches 4 of (7x+6)/(3x-2)	\lim\:_{x\to\:4}(\frac{7x+6}{3x-2})
derivative of (x^{3/2}^2)	\frac{d}{dx}((x^{\frac{3}{2}})^{2})
integral of (x^2-5x+16)/((2x+1)(x-2)^2)	\int\:\frac{x^{2}-5x+16}{(2x+1)(x-2)^{2}}dx
(\partial)/(\partial y)(e^xy)	\frac{\partial\:}{\partial\:y}(e^{x}y)
(xdy)/(dx)+y= 1/(y^2)	\frac{xdy}{dx}+y=\frac{1}{y^{2}}
derivative of \sqrt[3]{a}	derivative\:\sqrt[3]{a}
tangent of f(x)=(x^2)/(x+4),\at x=2	tangent\:f(x)=\frac{x^{2}}{x+4},\at\:x=2
(dy)/(dx)-2y=4-x	\frac{dy}{dx}-2y=4-x
derivative of e^{-t/2}-(e^{-t/2}t)/2	derivative\:e^{-\frac{t}{2}}-\frac{e^{-\frac{t}{2}}t}{2}
tangent of y=8sqrt(x)-6,(64,58)	tangent\:y=8\sqrt{x}-6,(64,58)
inverse oflaplace 1/(s^2+6s+25)	inverselaplace\:\frac{1}{s^{2}+6s+25}
integral of (cos(3x)-sin(x))	\int\:(\cos(3x)-\sin(x))dx
integral from-infinity to 0 of 1/(2-5x)	\int\:_{-\infty\:}^{0}\frac{1}{2-5x}dx
derivative of y=x^3-2x+1	derivative\:y=x^{3}-2x+1
integral of 1/((9-x)^{3/2)}	\int\:\frac{1}{(9-x)^{\frac{3}{2}}}dx
integral of sin(3/4)xcos^2(3/4)x	\int\:\sin(\frac{3}{4})x\cos^{2}(\frac{3}{4})xdx
sum from n=1(1-1/n) to infinity of n^2	\sum\:_{n=1(1-\frac{1}{n})}^{\infty\:}n^{2}
integral from 2 to 4 of (2x-3)(3x+1)	\int\:_{2}^{4}(2x-3)(3x+1)dx
derivative of 1/(y^2)(yx+x^2)	derivative\:\frac{1}{y^{2}}\cdot\:(y\cdot\:x+x^{2})
integral of 2r^2	\int\:2r^{2}dr
derivative of xcos(1-e^x)	derivative\:x\cos(1-e^{x})
integral of (7/(x^5)+4x+3)	\int\:(\frac{7}{x^{5}}+4x+3)dx
derivative of ln(xsqrt(x))	derivative\:\ln(x\sqrt{x})
tangent of 18sqrt(x)-3x	tangent\:18\sqrt{x}-3x
(dy)/(dt)+4y=2e^{-3t}	\frac{dy}{dt}+4y=2e^{-3t}
derivative of x^{52}-1/(x^2)	\frac{d}{dx}(x^{52}-\frac{1}{x^{2}})
longdivision (x^2-1)/(2x-3)	longdivision\:\frac{x^{2}-1}{2x-3}
integral of 5e^{4x+e^{4x}}	\int\:5e^{4x+e^{4x}}dx
derivative of f(x)=(x^3+3x+6)(4+1/(x^2))	derivative\:f(x)=(x^{3}+3x+6)(4+\frac{1}{x^{2}})
integral of cos(x/4)sin(x/4)	\int\:\cos(\frac{x}{4})\sin(\frac{x}{4})dx
integral of (x+3)/(x^2-6x+5)	\int\:\frac{x+3}{x^{2}-6x+5}dx
derivative of ln(5x+7)	\frac{d}{dx}(\ln(5x+7))
integral of tan(4xse)c^24x	\int\:\tan(4xse)c^{2}4xdx

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