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Popular Calculus Problems

derivative of (d/(dx(sin(x)))/x)	\frac{d}{dx}(\frac{\frac{d}{dx}(\sin(x))}{x})
y^{''}+5y^'+6y=sin(e^x)	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=\sin(e^{x})
sum from n=1 to infinity of (1/9)^n	\sum\:_{n=1}^{\infty\:}(\frac{1}{9})^{n}
derivative of y=(5t)/(\sqrt[4]{t^3)}	derivative\:y=\frac{5t}{\sqrt[4]{t^{3}}}
integral from-1 to 1 of e^y-(y^2-4)	\int\:_{-1}^{1}e^{y}-(y^{2}-4)dy
integral of 4e^x+cos(x/5)	\int\:4e^{x}+\cos(\frac{x}{5})dx
integral of 1/(sqrt(5+x^2))	\int\:\frac{1}{\sqrt{5+x^{2}}}dx
integral of (tan^4(x))/(sec^7(x))	\int\:\frac{\tan^{4}(x)}{\sec^{7}(x)}dx
integral of 3sin^2(t)cos(t)	\int\:3\sin^{2}(t)\cos(t)dt
integral of x^4e^{3x}	\int\:x^{4}e^{3x}dx
derivative of 2sec(2xtan(2x))	\frac{d}{dx}(2\sec(2x)\tan(2x))
derivative of 0.125xsqrt(64-x^2)	derivative\:0.125x\sqrt{64-x^{2}}
(\partial)/(\partial x)(x^2+sin(xy))	\frac{\partial\:}{\partial\:x}(x^{2}+\sin(xy))
derivative of acos(bx)	\frac{d}{dx}(a\cos(bx))
integral of 4sqrt(x)-4/(sqrt(x))	\int\:4\sqrt{x}-\frac{4}{\sqrt{x}}dx
integral from 1 to 4 of (x^2+1/(4x^2))	\int\:_{1}^{4}(x^{2}+\frac{1}{4x^{2}})dx
t(dy)/(dt)+5y=t	t\frac{dy}{dt}+5y=t
integral of (3x-1)/((3x^2-2x+1)^4)	\int\:\frac{3x-1}{(3x^{2}-2x+1)^{4}}dx
derivative of sqrt((Inx+1/(Inx-1)))	\frac{d}{dx}(\sqrt{\frac{Inx+1}{Inx-1}})
integral from 0 to 1 of 1/2 e^{-2x}	\int\:_{0}^{1}\frac{1}{2}e^{-2x}dx
integral from-2 to 2 of 1/2 (16-x^4)	\int\:_{-2}^{2}\frac{1}{2}(16-x^{4})dx
integral of cos(3x+4)	\int\:\cos(3x+4)dx
integral of (sqrt(x)+ln(x))/x	\int\:\frac{\sqrt{x}+\ln(x)}{x}dx
derivative of a/(x^b)	\frac{d}{dx}(\frac{a}{x^{b}})
limit as x approaches-4 of 1/(x^2-16)	\lim\:_{x\to\:-4}(\frac{1}{x^{2}-16})
(1+x^4)(dy)/(dx)=2x^3(1-y^2)	(1+x^{4})\frac{dy}{dx}=2x^{3}(1-y^{2})
sum from n=0 to infinity of 1/(2^{2n-1)}	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{2n-1}}
integral from 0 to a of 1/((a+r-x)^2)	\int\:_{0}^{a}\frac{1}{(a+r-x)^{2}}dx
area x,x^3	area\:x,x^{3}
integral of (sin(x))/(cos^6(x))	\int\:\frac{\sin(x)}{\cos^{6}(x)}dx
inverse oflaplace-(20)/(s(s+10))	inverselaplace\:-\frac{20}{s(s+10)}
derivative of y=2x^3+3x^2-12x+3	derivative\:y=2x^{3}+3x^{2}-12x+3
derivative of sqrt(5x^6-12)	\frac{d}{dx}(\sqrt{5x^{6}-12})
integral of e^{5x}cos(8x)	\int\:e^{5x}\cos(8x)dx
integral from (11pi)/2 to 6pi of 9sin(x)	\int\:_{\frac{11π}{2}}^{6π}9\sin(x)dx
y^'=(1-y)cos(x)	y^{\prime\:}=(1-y)\cos(x)
integral of y/(sqrt(x))	\int\:\frac{y}{\sqrt{x}}dx
tangent of y=(x^3-16x)^8,(-4,0)	tangent\:y=(x^{3}-16x)^{8},(-4,0)
(dy)/(dx)=(x+y)	\frac{dy}{dx}=(x+y)
derivative of x(ln(x^2))	\frac{d}{dx}(x(\ln(x^{2})))
integral of sin^6(2x)	\int\:\sin^{6}(2x)dx
x^{''}+3x^'+4x=0,x(0)=3,x^'(0)=1	x^{\prime\:\prime\:}+3x^{\prime\:}+4x=0,x(0)=3,x^{\prime\:}(0)=1
derivative of-(e^{-\|x\|}x/(\|x\|))	\frac{d}{dx}(-\frac{e^{-\left\|x\right\|}x}{\left\|x\right\|})
(\partial)/(\partial x)(2t^2+2x)	\frac{\partial\:}{\partial\:x}(2t^{2}+2x)
(\partial)/(\partial x)(2y-3x)	\frac{\partial\:}{\partial\:x}(2y-3x)
derivative of 4x^2-2x-1	derivative\:4x^{2}-2x-1
y^'=e^y	y^{\prime\:}=e^{y}
limit as x approaches 2 of (x+1)/(2-x)	\lim\:_{x\to\:2}(\frac{x+1}{2-x})
integral of 4x^{1/3}	\int\:4x^{\frac{1}{3}}dx
derivative of 4sin(2x-3cos(3x))	\frac{d}{dx}(4\sin(2x)-3\cos(3x))
integral from-2 to 0 of-x^2-2x	\int\:_{-2}^{0}-x^{2}-2xdx
inverse oflaplace 1/(s(s^2+s+1))	inverselaplace\:\frac{1}{s(s^{2}+s+1)}
(\partial)/(\partial x)(1/(x^2)c)	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}}c)
derivative of f(x)=3x-5	derivative\:f(x)=3x-5
integral from-2 to 2 of (6x)-(x^2-7)	\int\:_{-2}^{2}(6x)-(x^{2}-7)dx
area y=x^2-4x,y=4x	area\:y=x^{2}-4x,y=4x
integral of (e^{2x})/(e^{2x)+4}	\int\:\frac{e^{2x}}{e^{2x}+4}dx
limit as x approaches 0 of (2^{3+x}-8)/x	\lim\:_{x\to\:0}(\frac{2^{3+x}-8}{x})
integral of x^2(3+x^3)^3	\int\:x^{2}(3+x^{3})^{3}dx
derivative of 5+sqrt(7x)	\frac{d}{dx}(5+\sqrt{7x})
integral of 1/((9x^2+16)^2)	\int\:\frac{1}{(9x^{2}+16)^{2}}dx
derivative of 2x(12-x^3)	\frac{d}{dx}(2x(12-x)^{3})
taylor ln(1+8x^2)	taylor\:\ln(1+8x^{2})
derivative of cos((1-e^{9x})/(1+e^{9x)})	derivative\:\cos(\frac{1-e^{9x}}{1+e^{9x}})
xy+y^2+x^2-x^2(dy)/(dx)=0	xy+y^{2}+x^{2}-x^{2}\frac{dy}{dx}=0
limit as x approaches+0 of 7	\lim\:_{x\to\:+0}(7)
limit as x approaches-4 of f(x)	\lim\:_{x\to\:-4}(f(x))
derivative of csc(x/2)	\frac{d}{dx}(\csc(\frac{x}{2}))
integral of x(arcsin(x))/(sqrt(1-x^2))	\int\:x\frac{\arcsin(x)}{\sqrt{1-x^{2}}}dx
integral of (cos(x))/(4-sin^2(x))	\int\:\frac{\cos(x)}{4-\sin^{2}(x)}dx
limit as x approaches 3 of ln(x-3)	\lim\:_{x\to\:3}(\ln(x-3))
limit as x approaches infinity of 1^{+x}	\lim\:_{x\to\:\infty\:}(1^{+x})
(d^2)/(dx^2)(xy)	\frac{d^{2}}{dx^{2}}(xy)
integral from 0 to ln(4) of e^x-e^{-3x}	\int\:_{0}^{\ln(4)}e^{x}-e^{-3x}dx
limit as x approaches+0 of (tan(x)-x)/x	\lim\:_{x\to\:+0}(\frac{\tan(x)-x}{x})
(\partial)/(\partial y)(x^5ln(y^5))	\frac{\partial\:}{\partial\:y}(x^{5}\ln(y^{5}))
(\partial)/(\partial x)(ln(6x))	\frac{\partial\:}{\partial\:x}(\ln(6x))
tangent of f(x)= 1/(x^2),(-3, 1/9)	tangent\:f(x)=\frac{1}{x^{2}},(-3,\frac{1}{9})
integral of 1/(cos^2(3x))	\int\:\frac{1}{\cos^{2}(3x)}dx
integral from-2 to 2 of (x+3)sqrt(4-x^2)	\int\:_{-2}^{2}(x+3)\sqrt{4-x^{2}}dx
integral of ((x^4+2x^3-3)/(x^3))	\int\:(\frac{x^{4}+2x^{3}-3}{x^{3}})dx
derivative of f(x)=sqrt(2e^{x^3)+1}	derivative\:f(x)=\sqrt{2e^{x^{3}}+1}
f(x)=sqrt(x)+3	f(x)=\sqrt{x}+3
derivative of sqrt(x)+5e^x	\frac{d}{dx}(\sqrt{x}+5e^{x})
limit as x approaches 2-of 1/(x+2)	\lim\:_{x\to\:2-}(\frac{1}{x+2})
derivative of-1/(cos^2(x))	\frac{d}{dx}(-\frac{1}{\cos^{2}(x)})
integral from 0 to pi/(18) of cos(9x)	\int\:_{0}^{\frac{π}{18}}\cos(9x)dx
integral of 11tan^3(x)	\int\:11\tan^{3}(x)dx
derivative of ln(sqrt(x^4-4x))	\frac{d}{dx}(\ln(\sqrt{x^{4}-4x}))
integral from 0 to 2 of pi(x+1)^2	\int\:_{0}^{2}π(x+1)^{2}dx
derivative of x^4+3x	\frac{d}{dx}(x^{4}+3x)
integral of (log_{3}(x))/x	\int\:\frac{\log_{3}(x)}{x}dx
y^'+((1+x)/x)y=0	y^{\prime\:}+(\frac{1+x}{x})y=0
tangent of y=ln(x^2),(5,ln(25))	tangent\:y=\ln(x^{2}),(5,\ln(25))
integral of 1/(x(\sqrt[7]{x))^1}	\int\:\frac{1}{x(\sqrt[7]{x})^{1}}dx
derivative of f(x)=3x^8	derivative\:f(x)=3x^{8}
limit as x approaches 0 of x^{sin(2x)}	\lim\:_{x\to\:0}(x^{\sin(2x)})
(\partial)/(\partial x)((4x)/(y^3))	\frac{\partial\:}{\partial\:x}(\frac{4x}{y^{3}})
x-ydx+xdy=0	x-ydx+xdy=0
integral from 0 to-pi/3 of xcos(3x)	\int\:_{0}^{-\frac{π}{3}}x\cos(3x)dx

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