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Popular Calculus Problems

integral of sqrt(4-9x^2)	\int\:\sqrt{4-9x^{2}}dx
derivative of e^{x-y}	derivative\:e^{x-y}
derivative of y=7	derivative\:y=7
integral of x^2(x^3+1)^{1/2}	\int\:x^{2}(x^{3}+1)^{\frac{1}{2}}dx
derivative of c^{1/2}	derivative\:c^{\frac{1}{2}}
slope of (-2)/x-(-4)/y =1	slope\:\frac{-2}{x}-\frac{-4}{y}=1
area y=3cos(3x),y=3-3cos(3x),0<= x<= pi/3	area\:y=3\cos(3x),y=3-3\cos(3x),0\le\:x\le\:\frac{π}{3}
derivative of e^{x^3+4x}	\frac{d}{dx}(e^{x^{3}+4x})
integral of (sqrt(x^2-361))/x	\int\:\frac{\sqrt{x^{2}-361}}{x}dx
integral from 0 to 2 of sqrt(36x+145)	\int\:_{0}^{2}\sqrt{36x+145}dx
laplacetransform t^2+6t-17	laplacetransform\:t^{2}+6t-17
(\partial)/(\partial x)(-x/((x+y)^2))	\frac{\partial\:}{\partial\:x}(-\frac{x}{(x+y)^{2}})
integral from 0 to+oo of x*(x+1)^{-2}	\int\:_{0}^{+oo}x\cdot\:(x+1)^{-2}dx
f(x)=5-x	f(x)=5-x
integral from 0 to 3 of sqrt(1+x)	\int\:_{0}^{3}\sqrt{1+x}dx
derivative of 3/(5x)	\frac{d}{dx}(\frac{3}{5x})
d/(dt)(sqrt(2)sin(t)+sqrt(2))	\frac{d}{dt}(\sqrt{2}\sin(t)+\sqrt{2})
derivative of e^{0.2x}	\frac{d}{dx}(e^{0.2x})
integral of x^4-2x^3+2	\int\:x^{4}-2x^{3}+2dx
integral of 16x^3cos(2-x^4)	\int\:16x^{3}\cos(2-x^{4})dx
d/(du)(cos(u))	\frac{d}{du}(\cos(u))
y^{''}+2y^'+y=0,y(0)=4,y^'(0)=-3	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(0)=4,y^{\prime\:}(0)=-3
derivative of (x^2-3x+1/(x^2))	\frac{d}{dx}(\frac{x^{2}-3x+1}{x^{2}})
limit as x approaches-1 of 8x^4-3x^3+7x	\lim\:_{x\to\:-1}(8x^{4}-3x^{3}+7x)
derivative of sin(x^2+2x-1)	\frac{d}{dx}(\sin(x^{2}+2x-1))
(\partial)/(\partial x)(ln(x+y))	\frac{\partial\:}{\partial\:x}(\ln(x+y))
derivative of 1/(3+x)	derivative\:\frac{1}{3+x}
derivative of x/(x^2-1)	derivative\:\frac{x}{x^{2}-1}
integral of 6e^{3x}-8/(e^{2x)}	\int\:6e^{3x}-\frac{8}{e^{2x}}dx
y^{''}-4y^'+4y=(x+1)e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=(x+1)e^{2x}
tangent of f(x)= 1/(sqrt(8x)),\at (x=9)	tangent\:f(x)=\frac{1}{\sqrt{8x}},\at\:(x=9)
sum from n=0 to infinity of (2^n)/((2n)!)x^{2n}	\sum\:_{n=0}^{\infty\:}\frac{2^{n}}{(2n)!}x^{2n}
limit as x approaches 7-of (x-7)/(\|x-7\|)	\lim\:_{x\to\:7-}(\frac{x-7}{\left\|x-7\right\|})
integral from 0 to 9 of (11e^{sqrt(x)})/(sqrt(x))	\int\:_{0}^{9}\frac{11e^{\sqrt{x}}}{\sqrt{x}}dx
(dy)/(dt)=t^2y^2	\frac{dy}{dt}=t^{2}y^{2}
integral of cos^2(15x)	\int\:\cos^{2}(15x)dx
integral of 2/(5x-1)	\int\:\frac{2}{5x-1}dx
(\partial)/(\partial y)(sqrt(3x^2+y^2))	\frac{\partial\:}{\partial\:y}(\sqrt{3x^{2}+y^{2}})
derivative of 6sqrt(x^7)	\frac{d}{dx}(6\sqrt{x^{7}})
derivative of 3ax+bx^3	\frac{d}{dx}(3ax+bx^{3})
(\partial)/(\partial x)(3x^2+5xy-7y^2+1)	\frac{\partial\:}{\partial\:x}(3x^{2}+5xy-7y^{2}+1)
derivative of e^{x^2+4}	\frac{d}{dx}(e^{x^{2}+4})
integral of x^2(6-x^3)	\int\:x^{2}(6-x^{3})dx
derivative of cos^2(2x+1)	\frac{d}{dx}(\cos^{2}(2x+1))
integral of 3/5	\int\:\frac{3}{5}dx
(\partial)/(\partial x)(x^2+y^2+z^2-2yz)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z^{2}-2yz)
derivative of d{y}(d,x)	\frac{d}{dx}(d{y}(d,x))
taylor 7/(sqrt(x)),4	taylor\:\frac{7}{\sqrt{x}},4
integral from 1 to 4 of sqrt(x)ln(x/2)	\int\:_{1}^{4}\sqrt{x}\ln(\frac{x}{2})dx
y^{'''}-6y^{''}+11y^'-6y=0	y^{\prime\:\prime\:\prime\:}-6y^{\prime\:\prime\:}+11y^{\prime\:}-6y=0
integral from-5 to 1 of (2x+6)	\int\:_{-5}^{1}(2x+6)dx
derivative of (sqrt(7))/t	derivative\:\frac{\sqrt{7}}{t}
laplacetransform 1/2 t^2	laplacetransform\:\frac{1}{2}t^{2}
area y=2x-1,x=2,x=5,y=0	area\:y=2x-1,x=2,x=5,y=0
derivative of-1/3 ln((tan(x/2-3)/3))	\frac{d}{dx}(-\frac{1}{3}\ln(\frac{\tan(\frac{x}{2})-3}{3}))
y^{''}+6y^'+8y=130cos(3t)	y^{\prime\:\prime\:}+6y^{\prime\:}+8y=130\cos(3t)
limit as x approaches-1/e of xln(e+1/x)	\lim\:_{x\to\:-\frac{1}{e}}(x\ln(e+\frac{1}{x}))
integral of xsqrt(1-2x)	\int\:x\sqrt{1-2x}dx
(\partial)/(\partial x)(x/(e^{x/y)})	\frac{\partial\:}{\partial\:x}(\frac{x}{e^{\frac{x}{y}}})
derivative of-2/((6x-7x^4^3))	\frac{d}{dx}(-\frac{2}{(6x-7x^{4})^{3}})
(dy)/(dx)=log_{10}(x)	\frac{dy}{dx}=\log_{10}(x)
(dy}{dx}=\frac{x^9-8y)/x	\frac{dy}{dx}=\frac{x^{9}-8y}{x}
integral from 6 to 12 of 2x-18	\int\:_{6}^{12}2x-18dx
integral of (5x+2)^3	\int\:(5x+2)^{3}dx
y^{''}+y=e^x	y^{\prime\:\prime\:}+y=e^{x}
(dy)/(dx)=((x^2-1))/(2y),y(3)=1	\frac{dy}{dx}=\frac{(x^{2}-1)}{2y},y(3)=1
(\partial)/(\partial y)(y^2e^{xyz})	\frac{\partial\:}{\partial\:y}(y^{2}e^{xyz})
(\partial)/(\partial x)(y^5-4xy)	\frac{\partial\:}{\partial\:x}(y^{5}-4xy)
y^'=(6y^3)/((3-2x)^2),y(0)=-1	y^{\prime\:}=\frac{6y^{3}}{(3-2x)^{2}},y(0)=-1
integral from 0 to 1 of ln(2x)	\int\:_{0}^{1}\ln(2x)dx
integral of (2/(x^2))	\int\:(\frac{2}{x^{2}})dx
(\partial)/(\partial x)(1/x-y/x)	\frac{\partial\:}{\partial\:x}(\frac{1}{x}-\frac{y}{x})
integral of tan^2(x)tan(x)	\int\:\tan^{2}(x)\tan(x)dx
integral of 7/((x-3)sqrt(x^2-6x+5))	\int\:\frac{7}{(x-3)\sqrt{x^{2}-6x+5}}dx
(\partial)/(\partial x)(e^{-x}sin(x))	\frac{\partial\:}{\partial\:x}(e^{-x}\sin(x))
derivative of 8/(x-5)	\frac{d}{dx}(\frac{8}{x-5})
f(x)=-csc^2(x)	f(x)=-\csc^{2}(x)
(x^2-y^2)dx+(2xy)dy=0	(x^{2}-y^{2})dx+(2xy)dy=0
integral of 1/(sqrt(-x^2+4x-3))	\int\:\frac{1}{\sqrt{-x^{2}+4x-3}}dx
integral of 15/4 x^2	\int\:\frac{15}{4}x^{2}dx
d/(dt)(log_{3}(2t-x))	\frac{d}{dt}(\log_{3}(2t-x))
tangent of y=2x^3+3x^2-12x+1	tangent\:y=2x^{3}+3x^{2}-12x+1
d/(d{r)}(sqrt({r)}+\sqrt[3]{{r}})	\frac{d}{d{r}}(\sqrt{{r}}+\sqrt[3]{{r}})
(\partial)/(\partial y)((2y)/(x^2-y^2))	\frac{\partial\:}{\partial\:y}(\frac{2y}{x^{2}-y^{2}})
derivative of cos(xsin(x))	derivative\:\cos(x\sin(x))
derivative of (-6x/(1-x))	\frac{d}{dx}(\frac{-6x}{1-x})
inverse oflaplace (s+4)/(s^2+6s+18)	inverselaplace\:\frac{s+4}{s^{2}+6s+18}
integral of ax^5	\int\:ax^{5}dx
area y=x^2,y=8-x^2,y=4x+11	area\:y=x^{2},y=8-x^{2},y=4x+11
limit as x approaches 3 of (x-2)^2	\lim\:_{x\to\:3}((x-2)^{2})
(dy)/(dx)= k/(x^2)	\frac{dy}{dx}=\frac{k}{x^{2}}
integral from 1 to 2 of (3ln(x))/(x^2)	\int\:_{1}^{2}\frac{3\ln(x)}{x^{2}}dx
(\partial)/(\partial x)(2y^2-3x^2-z)	\frac{\partial\:}{\partial\:x}(2y^{2}-3x^{2}-z)
derivative of log_{e}(sqrt(x^2+1))	\frac{d}{dx}(\log_{e}(\sqrt{x^{2}+1}))
derivative of y=(tan(-1(3x)))2	derivative\:y=(\tan(-1(3x)))2
derivative of \sqrt[x]{x}	derivative\:\sqrt[x]{x}
derivative of-0.6t^2+30t	derivative\:-0.6t^{2}+30t
integral from 0 to 5 of pi(-3/5 x+3)^2	\int\:_{0}^{5}π(-\frac{3}{5}x+3)^{2}dx
derivative of (t^3+3t)/(t^2-4t+3)	derivative\:\frac{t^{3}+3t}{t^{2}-4t+3}
integral of 7/(x(x-7)^2)	\int\:\frac{7}{x(x-7)^{2}}dx

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