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Popular Calculus Problems

taylor sqrt(1+x),1	taylor\:\sqrt{1+x},1
integral of 1/4 cos^2(2x)	\int\:\frac{1}{4}\cos^{2}(2x)dx
y^'+0.2*y=5	y^{\prime\:}+0.2\cdot\:y=5
derivative of f(x)=x^{1/6}	derivative\:f(x)=x^{\frac{1}{6}}
integral of x(x^2+2)	\int\:x(x^{2}+2)dx
integral of tsqrt(4+9t^2)	\int\:t\sqrt{4+9t^{2}}dt
integral of 1/(1+64x^2)	\int\:\frac{1}{1+64x^{2}}dx
integral from 0 to infinity of te^{-t^2}	\int\:_{0}^{\infty\:}te^{-t^{2}}dt
derivative of x/(x-9)	\frac{d}{dx}(\frac{x}{x-9})
integral of (3x-5)^{1/2}	\int\:(3x-5)^{\frac{1}{2}}dx
y^{''}=6x-12	y^{\prime\:\prime\:}=6x-12
area y=6x^4-6x^2,y=3x^2	area\:y=6x^{4}-6x^{2},y=3x^{2}
(d^2x)/(dt^2)+2(dx)/(dt)+2x=sin(2t)	\frac{d^{2}x}{dt^{2}}+2\frac{dx}{dt}+2x=\sin(2t)
(dy)/(dx)= 1/(2cos^2(x))	\frac{dy}{dx}=\frac{1}{2\cos^{2}(x)}
(dy)/(dx)=y(1-2y)	\frac{dy}{dx}=y(1-2y)
integral from 0 to 1 of x(x^2-1)e^{-x^2}	\int\:_{0}^{1}x(x^{2}-1)e^{-x^{2}}dx
integral from 0 to 3 of (sqrt(x))	\int\:_{0}^{3}(\sqrt{x})dx
integral of 1/(sqrt(x)(1-3\sqrt{x))}	\int\:\frac{1}{\sqrt{x}(1-3\sqrt{x})}dx
integral of 8x(4x^2+5)^6	\int\:8x(4x^{2}+5)^{6}dx
integral of 4/(7^{ln(x))}	\int\:\frac{4}{7^{\ln(x)}}dx
limit as x approaches 0+of ln(x^x)	\lim\:_{x\to\:0+}(\ln(x^{x}))
integral of cos(x)csc(x)	\int\:\cos(x)\csc(x)dx
derivative of x^2*{f}(x)	\frac{d}{dx}(x^{2}\cdot\:{f}(x))
derivative of e^{-arcsinh(x/2})	\frac{d}{dx}(e^{-\arcsinh(\frac{x}{2})})
derivative of (sqrt(x))/(6x-6)	derivative\:\frac{\sqrt{x}}{6x-6}
derivative of \|x\|^3	\frac{d}{dx}(\left\|x\right\|^{3})
integral of 1/(sqrt((4x-x^2)^3))	\int\:\frac{1}{\sqrt{(4x-x^{2})^{3}}}dx
integral of e^{-t(a+s)}	\int\:e^{-t(a+s)}dt
integral from 50 to 50.25 of 2	\int\:_{50}^{50.25}2dx
derivative of f(x)=2x^5	derivative\:f(x)=2x^{5}
sum from n=1 to infinity of ln(1+1/n)	\sum\:_{n=1}^{\infty\:}\ln(1+\frac{1}{n})
integral from 0 to 9 of sqrt(81-x^2)	\int\:_{0}^{9}\sqrt{81-x^{2}}dx
integral of 1/(x^2sqrt(2x^2+32))	\int\:\frac{1}{x^{2}\sqrt{2x^{2}+32}}dx
64y^{''}+144y^'+81y=0	64y^{\prime\:\prime\:}+144y^{\prime\:}+81y=0
inverse oflaplace (10)/(s^2+s+10)*1/s	inverselaplace\:\frac{10}{s^{2}+s+10}\cdot\:\frac{1}{s}
(\partial)/(\partial x)((e^y)/(x+y^5))	\frac{\partial\:}{\partial\:x}(\frac{e^{y}}{x+y^{5}})
(\partial)/(\partial x)(cos(2cx+act))	\frac{\partial\:}{\partial\:x}(\cos(2cx+act))
derivative of 1000(1-x/(60)^2)	\frac{d}{dx}(1000(1-\frac{x}{60})^{2})
y^'=1+y/x	y^{\prime\:}=1+\frac{y}{x}
y^{''}-y=-x	y^{\prime\:\prime\:}-y=-x
integral of e^{x^{-1}}	\int\:e^{x^{-1}}dx
tangent of y=x^3-7x^2+16x+7,\at	tangent\:y=x^{3}-7x^{2}+16x+7,\at\:
derivative of (6x/(7-tan(x)))	\frac{d}{dx}(\frac{6x}{7-\tan(x)})
(-8cos(2x))^'	(-8\cos(2x))^{\prime\:}
f(x)=sqrt(1+x)	f(x)=\sqrt{1+x}
derivative of x(3x+2^4)	\frac{d}{dx}(x(3x+2)^{4})
(\partial)/(\partial x)(9xln(x)y)	\frac{\partial\:}{\partial\:x}(9x\ln(x)y)
slope of (-4-4)(-4-9)	slope\:(-4-4)(-4-9)
ty^'=y+((1/4)t^2+y^2)^{(1/2)}	t\cdot\:y^{\prime\:}=y+((\frac{1}{4})\cdot\:t^{2}+y^{2})^{(\frac{1}{2})}
integral of 1/(xsqrt(9-16x^2))	\int\:\frac{1}{x\sqrt{9-16x^{2}}}dx
integral of (x^2+2x+4)	\int\:(x^{2}+2x+4)dx
integral from x/z to 1 of 1	\int\:_{\frac{x}{z}}^{1}1dy
derivative of-5e^{x+3}+e^1	derivative\:-5e^{x+3}+e^{1}
(\partial)/(\partial x)(1/(2pi)(y/x)^{1/2})	\frac{\partial\:}{\partial\:x}(\frac{1}{2π}(\frac{y}{x})^{\frac{1}{2}})
derivative of ae^{3x}	\frac{d}{dx}(ae^{3x})
derivative of s(t)= 1/5 t^4	derivative\:s(t)=\frac{1}{5}t^{4}
derivative of (7-3x^2)^3	derivative\:(7-3x^{2})^{3}
derivative of (x+36/(sqrt(x)))	\frac{d}{dx}(\frac{x+36}{\sqrt{x}})
(\partial)/(\partial x)(6e^ysin(4x)+3y-2xy)	\frac{\partial\:}{\partial\:x}(6e^{y}\sin(4x)+3y-2xy)
integral of 2-x^2-x	\int\:2-x^{2}-xdx
integral of (10000-5000x)/((x^2-4x+5)^2)	\int\:\frac{10000-5000x}{(x^{2}-4x+5)^{2}}dx
sum from n=0 to infinity of (n!)/(104^n)	\sum\:_{n=0}^{\infty\:}\frac{n!}{104^{n}}
derivative of f(x)=((1))/((1+x^2))	derivative\:f(x)=\frac{(1)}{(1+x^{2})}
integral of (e^tcos(e^t))/(3+3sin(e^t))	\int\:\frac{e^{t}\cos(e^{t})}{3+3\sin(e^{t})}dt
limit as x approaches+(-11) of x^2+11	\lim\:_{x\to\:+(-11)}(x^{2}+11)
integral of cos^2(7x)	\int\:\cos^{2}(7x)dx
integral of e^{6x+2}	\int\:e^{6x+2}dx
integral of e^{x+4e^x}	\int\:e^{x+4e^{x}}dx
integral of x/(sqrt(2-5x^2))	\int\:\frac{x}{\sqrt{2-5x^{2}}}dx
y=(-x+3)^3	y=(-x+3)^{3}
integral of xsin((npix)/l)	\int\:x\sin(\frac{nπx}{l})dx
area f(x)=x^2+8,(-2,1)	area\:f(x)=x^{2}+8,(-2,1)
integral from-1 to 4 of 3x^2-x	\int\:_{-1}^{4}3x^{2}-xdx
integral of (20)/(1-cos(5x))	\int\:\frac{20}{1-\cos(5x)}dx
limit as x approaches pi/6 of cos(x)	\lim\:_{x\to\:\frac{π}{6}}(\cos(x))
limit as t approaches 1 of sqrt(t+2)	\lim\:_{t\to\:1}(\sqrt{t+2})
derivative of 1/(cot(x))	\frac{d}{dx}(\frac{1}{\cot(x)})
derivative of (-4x^2+9^2)	\frac{d}{dx}((-4x^{2}+9)^{2})
d/(dy)(xcos(x)y)	\frac{d}{dy}(x\cos(x)y)
integral of ((sin^2(x)))/(x^2)	\int\:\frac{(\sin^{2}(x))}{x^{2}}dx
derivative of (x^2+2x-8)/(x-1)	derivative\:\frac{x^{2}+2x-8}{x-1}
integral of (a^{ln(x)})/x	\int\:\frac{a^{\ln(x)}}{x}dx
derivative of 1/(1-5x^2)	derivative\:\frac{1}{1-5x^{2}}
derivative of sqrt(-2x)	\frac{d}{dx}(\sqrt{-2x})
integral of 1/((x^2-1)^3)	\int\:\frac{1}{(x^{2}-1)^{3}}dx
y^{''}+(14)/t y^'+(42)/(t^2)y=0	y^{\prime\:\prime\:}+\frac{14}{t}y^{\prime\:}+\frac{42}{t^{2}}y=0
(d^2)/(dx^2)(3^x)	\frac{d^{2}}{dx^{2}}(3^{x})
derivative of sin(e^{x^2}*cos(x))	\frac{d}{dx}(\sin(e^{x^{2}})\cdot\:\cos(x))
integral of 1/(x^3-3x^2)	\int\:\frac{1}{x^{3}-3x^{2}}dx
derivative of sqrt(x^2-3x+12)	\frac{d}{dx}(\sqrt{x^{2}-3x+12})
tangent of f(x)=2sin(x),\at x=(3pi)/4	tangent\:f(x)=2\sin(x),\at\:x=\frac{3π}{4}
y^'=sin(5x),y(0)=2	y^{\prime\:}=\sin(5x),y(0)=2
(\partial)/(\partial x)(x^2+y^2+z^2-3xyz)	\frac{\partial\:}{\partial\:x}(x^{2}+y^{2}+z^{2}-3xyz)
(x+1)(dy)/(dx)+(x+2)y=8xe^{-x}	(x+1)\frac{dy}{dx}+(x+2)y=8xe^{-x}
(\partial)/(\partial x)(5x^3yz^2)	\frac{\partial\:}{\partial\:x}(5x^{3}yz^{2})
integral of \sqrt[3]{x^4}	\int\:\sqrt[3]{x^{4}}dx
integral from-1 to 2 of x^3-1	\int\:_{-1}^{2}x^{3}-1dx
limit as x approaches 0 of x^4	\lim\:_{x\to\:0}(x^{4})
integral of x^2cos(5x)	\int\:x^{2}\cos(5x)dx
tangent of f(x)=2sin(x),(pi/6 ,1)	tangent\:f(x)=2\sin(x),(\frac{π}{6},1)

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