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Popular Calculus Problems

derivative of e^{2sin(x})	\frac{d}{dx}(e^{2\sin(x)})
integral of 3picos^3(5pix)sin^7(5pix)	\int\:3π\cos^{3}(5πx)\sin^{7}(5πx)dx
area y= 2/x ,y=8x,y= 1/(8x)	area\:y=\frac{2}{x},y=8x,y=\frac{1}{8x}
x(dy)/(dx)-y=sqrt(x^2+y^2)	x\frac{dy}{dx}-y=\sqrt{x^{2}+y^{2}}
(4du)/(dt)=u^2	\frac{4du}{dt}=u^{2}
derivative of e^{2x}+ln(2x)	\frac{d}{dx}(e^{2x}+\ln(2x))
y^{''}-4y^'+8y=0	y^{\prime\:\prime\:}-4y^{\prime\:}+8y=0
f(x)=arcsin(x/4)	f(x)=\arcsin(\frac{x}{4})
integral of x^{-1/6}	\int\:x^{-\frac{1}{6}}dx
xy^'+y=8xy^2	xy^{\prime\:}+y=8xy^{2}
derivative of (3x)/(8-cot(x))	derivative\:\frac{3x}{8-\cot(x)}
derivative of f(x)=5^{-x/2}sin(2x)	derivative\:f(x)=5^{-\frac{x}{2}}\sin(2x)
integral from 1 to 3 of r^3ln(r)	\int\:_{1}^{3}r^{3}\ln(r)dr
derivative of 4^{sin^2(x)+cos(3x)}	derivative\:4^{\sin^{2}(x)+\cos(3x)}
limit as x approaches 0 of (4x)/(sqrt(4+x)-\sqrt{4-x)}	\lim\:_{x\to\:0}(\frac{4x}{\sqrt{4+x}-\sqrt{4-x}})
integral of (2x-4)/(x^2+4)	\int\:\frac{2x-4}{x^{2}+4}dx
derivative of 2sqrt(4-x^2)	\frac{d}{dx}(2\sqrt{4-x^{2}})
implicit (dy)/(dx),sqrt(x+y)+xy=21	implicit\:\frac{dy}{dx},\sqrt{x+y}+xy=21
derivative of x^2cos(xy)	\frac{d}{dx}(x^{2}\cos(xy))
derivative of cos(7pix)	\frac{d}{dx}(\cos(7πx))
integral of sin^{1/2}(x)cos^3(x)	\int\:\sin^{\frac{1}{2}}(x)\cos^{3}(x)dx
limit as n approaches infinity of \sum_{i=1}^n(i^3)/(n^4)+1/n	\lim\:_{n\to\:\infty\:}(\sum\:_{i=1}^{n}\frac{i^{3}}{n^{4}}+\frac{1}{n})
derivative of xcos(y-ye^x)	\frac{d}{dx}(x\cos(y)-ye^{x})
limit as x approaches 5 of (x^2-7x+10)/(x^2-25)	\lim\:_{x\to\:5}(\frac{x^{2}-7x+10}{x^{2}-25})
(dy)/(dx)=(2y+sqrt(x^2-y^2))/(2x)	\frac{dy}{dx}=\frac{2y+\sqrt{x^{2}-y^{2}}}{2x}
integral of (sec^6(x))/(tan^3(x))	\int\:\frac{\sec^{6}(x)}{\tan^{3}(x)}dx
limit as x approaches 0-of e^{3/x}	\lim\:_{x\to\:0-}(e^{\frac{3}{x}})
limit as x approaches 0 of (x+5)/(3x)	\lim\:_{x\to\:0}(\frac{x+5}{3x})
derivative of (x^2)/(x-9)	derivative\:\frac{x^{2}}{x-9}
(x^3+3y)dx-xdy=0	(x^{3}+3y)dx-xdy=0
integral of (e^x)/((e^x-9)(e^{2x)+1)}	\int\:\frac{e^{x}}{(e^{x}-9)(e^{2x}+1)}dx
derivative of 1/6	\frac{d}{dx}(\frac{1}{6})
derivative of (1+4x^2)(x-x^2)	derivative\:(1+4x^{2})(x-x^{2})
derivative of Acos(x+Bsin(x))	\frac{d}{dx}(A\cos(x)+B\sin(x))
integral from-1 to 6 of-x^2+5x+6	\int\:_{-1}^{6}-x^{2}+5x+6dx
area y= 1/2 x,y= 6/x	area\:y=\frac{1}{2}x,y=\frac{6}{x}
derivative of 6x^5ln(x+x^5)	\frac{d}{dx}(6x^{5}\ln(x)+x^{5})
limit as x approaches 0 of (1-cos(4x))/x	\lim\:_{x\to\:0}(\frac{1-\cos(4x)}{x})
derivative of 3(4e^{2x}x+4e^{2x})	\frac{d}{dx}(3(4e^{2x}x+4e^{2x}))
integral of 7sin^4(x)cos^2(x)	\int\:7\sin^{4}(x)\cos^{2}(x)dx
(dy)/(dx)=(e^x)/(7+e^x)	\frac{dy}{dx}=\frac{e^{x}}{7+e^{x}}
integral of x^6e^{2x}	\int\:x^{6}e^{2x}dx
derivative of 3/((x+1))	derivative\:\frac{3}{(x+1)}
integral of u/2	\int\:\frac{u}{2}du
integral of t^7e^{t^4}	\int\:t^{7}e^{t^{4}}dt
integral of x^2*e^{-2x}	\int\:x^{2}\cdot\:e^{-2x}dx
derivative of y=xsin(2x)	derivative\:y=x\sin(2x)
integral of (4x)/((3x^2-1)^5)	\int\:\frac{4x}{(3x^{2}-1)^{5}}dx
integral of e^{3x}sin(6x)	\int\:e^{3x}\sin(6x)dx
derivative of 250000+15000x-0.3x^3	derivative\:250000+15000x-0.3x^{3}
derivative of ln(5x+ln(3x))	derivative\:\ln(5x+\ln(3x))
derivative of 1700e^x	\frac{d}{dx}(1700e^{x})
integral of 3sin(2θ)	\int\:3\sin(2θ)dθ
y^{''}-6y^'+13=0	y^{\prime\:\prime\:}-6y^{\prime\:}+13=0
integral of (37)/(37+e^x)	\int\:\frac{37}{37+e^{x}}dx
derivative of f(x)=7ln(x)	derivative\:f(x)=7\ln(x)
integral of cos((pix)/3)	\int\:\cos(\frac{πx}{3})dx
integral of arctan(x/3)	\int\:\arctan(\frac{x}{3})dx
derivative of y=(4x^2+6x+2)/(sqrt(x))	derivative\:y=\frac{4x^{2}+6x+2}{\sqrt{x}}
derivative of 2x(sin(x+cos(x)))	\frac{d}{dx}(2x(\sin(x)+\cos(x)))
integral of 3cos(2x)	\int\:3\cos(2x)dx
derivative of f(x)=ln(2x)	derivative\:f(x)=\ln(2x)
integral of 4t^2	\int\:4t^{2}dt
integral of (1/x-5/(4x^2+1))	\int\:(\frac{1}{x}-\frac{5}{4x^{2}+1})dx
integral of ((17))/((x-1)(x^2+16))	\int\:\frac{(17)}{(x-1)(x^{2}+16)}dx
integral of x(3x^2-2)	\int\:x(3x^{2}-2)dx
derivative of 1/5 x^5-3x^4+9x^2+1	\frac{d}{dx}(\frac{1}{5}x^{5}-3x^{4}+9x^{2}+1)
(dy)/(dx)=3xy^2	\frac{dy}{dx}=3xy^{2}
inverse oflaplace (2s)/((s-1)(s^2+25))	inverselaplace\:\frac{2s}{(s-1)(s^{2}+25)}
x((dy)/(dx))=sqrt(x^2-4)	x(\frac{dy}{dx})=\sqrt{x^{2}-4}
derivative of f(x)=(5x^2-7x)e^x	derivative\:f(x)=(5x^{2}-7x)e^{x}
derivative of 2^{sin(pix})	\frac{d}{dx}(2^{\sin(πx)})
integral of cos(x)sin(t-x)	\int\:\cos(x)\sin(t-x)dx
integral from-pi to pi of sin(2x)sin(2x)	\int\:_{-π}^{π}\sin(2x)\sin(2x)dx
y^{''}-7y^'+14y=-784t^2	y^{\prime\:\prime\:}-7y^{\prime\:}+14y=-784t^{2}
y^{''}+9y=3tan(3x)	y^{\prime\:\prime\:}+9y=3\tan(3x)
derivative of \sqrt[4]{(x^2+1/(x^2-1)})	\frac{d}{dx}(\sqrt[4]{\frac{x^{2}+1}{x^{2}-1}})
d/(ds)(s/(s^2+1))	\frac{d}{ds}(\frac{s}{s^{2}+1})
integral of sqrt(m+ny)	\int\:\sqrt{m+ny}dy
limit as x approaches e of ln\|3x\|	\lim\:_{x\to\:e}(\ln\left\|3x\right\|)
ydx+(ycos(x/y)-x)dy=0	ydx+(y\cos(\frac{x}{y})-x)dy=0
derivative of 1/5 sin(5x)	\frac{d}{dx}(\frac{1}{5}\sin(5x))
integral of 1/(sin^2(5x))	\int\:\frac{1}{\sin^{2}(5x)}dx
(dt)/(dt)	\frac{dt}{dt}
integral of sin(r^2)r	\int\:\sin(r^{2})rdr
limit as x approaches infinity of 0.5x^2	\lim\:_{x\to\:\infty\:}(0.5x^{2})
derivative of 4x^{2pi}	\frac{d}{dx}(4x^{2π})
limit as x approaches 0 of (arcsin(3x))/(arctan(5x))	\lim\:_{x\to\:0}(\frac{\arcsin(3x)}{\arctan(5x)})
derivative of sqrt(xe^x)	\frac{d}{dx}(\sqrt{xe^{x}})
integral of (-7x^2)/(sqrt(4x-x^2))	\int\:\frac{-7x^{2}}{\sqrt{4x-x^{2}}}dx
derivative of cos(15x)	\frac{d}{dx}(\cos(15x))
integral of arctan(6x)	\int\:\arctan(6x)dx
limit as x approaches 0 of (cos(2x))^{1/(x^2)}	\lim\:_{x\to\:0}((\cos(2x))^{\frac{1}{x^{2}}})
inverse oflaplace ((s+2))/(s^2+7s+12)	inverselaplace\:\frac{(s+2)}{s^{2}+7s+12}
integral of sin^2(8x)cos^2(8x)	\int\:\sin^{2}(8x)\cos^{2}(8x)dx
derivative of sqrt(9x^2)	\frac{d}{dx}(\sqrt{9x^{2}})
integral of-cos(x)3x^2	\int\:-\cos(x)3x^{2}dx
integral of 1/(3x+6)	\int\:\frac{1}{3x+6}dx
limit as x approaches 1-of 1/(x-1)	\lim\:_{x\to\:1-}(\frac{1}{x-1})
derivative of pi*x	\frac{d}{dx}(π\cdot\:x)

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