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Popular Calculus Problems

(dy)/(dx)+2xy=2x^3	\frac{dy}{dx}+2xy=2x^{3}
inverse oflaplace (3(s+3))/(s^2+6s+8)	inverselaplace\:\frac{3(s+3)}{s^{2}+6s+8}
limit as x approaches infinity of 3^x-x	\lim\:_{x\to\:\infty\:}(3^{x}-x)
sum from n=1 to infinity of n/(3n+2)	\sum\:_{n=1}^{\infty\:}\frac{n}{3n+2}
(\partial)/(\partial x)(y^5cos(6x)*6)	\frac{\partial\:}{\partial\:x}(y^{5}\cos(6x)\cdot\:6)
derivative of (1+ln(x)/(1-ln(x)))	\frac{d}{dx}(\frac{1+\ln(x)}{1-\ln(x)})
integral of 4/(4-x^2)	\int\:\frac{4}{4-x^{2}}dx
tangent of-(6x)/(x^2+1),\at x=1	tangent\:-\frac{6x}{x^{2}+1},\at\:x=1
derivative of f(x)=9x^2	derivative\:f(x)=9x^{2}
integral of x/(1-5x^2)	\int\:\frac{x}{1-5x^{2}}dx
derivative of 1/(sqrt(x^{13)})	\frac{d}{dx}(\frac{1}{\sqrt{x^{13}}})
integral of 4tan^3(x)sec(x)	\int\:4\tan^{3}(x)\sec(x)dx
integral from-1 to 0 of (x+1)^3	\int\:_{-1}^{0}(x+1)^{3}dx
derivative of 7x-4	\frac{d}{dx}(7x-4)
(y^3-1)exdx+3y^2(ex+1)dy=0	(y^{3}-1)exdx+3y^{2}(ex+1)dy=0
limit as x approaches 0 of 4xcot(x)	\lim\:_{x\to\:0}(4x\cot(x))
integral from 0 to 1 of 8e^{2sqrt(x)}	\int\:_{0}^{1}8e^{2\sqrt{x}}dx
derivative of 2e^x+8/(\sqrt[3]{x)}	derivative\:2e^{x}+\frac{8}{\sqrt[3]{x}}
derivative of ln(x^2e^{-x})	\frac{d}{dx}(\ln(x^{2}e^{-x}))
slope of xy-2y^2=5,(11,5)	slope\:xy-2y^{2}=5,(11,5)
integral from 1 to 2 of 9/(x^3+4x)	\int\:_{1}^{2}\frac{9}{x^{3}+4x}dx
derivative of 5/2 x^2	\frac{d}{dx}(\frac{5}{2}x^{2})
tangent of y=-6/x ,\at x=-4	tangent\:y=-\frac{6}{x},\at\:x=-4
derivative of cot^2(3x)	\frac{d}{dx}(\cot^{2}(3x))
sum from n=5 to infinity of e^{3-4n}	\sum\:_{n=5}^{\infty\:}e^{3-4n}
y^{''}+4pi^2y=cos^3(2pix)	y^{\prime\:\prime\:}+4π^{2}y=\cos^{3}(2πx)
integral of 2xInx^2	\int\:2xInx^{2}dx
derivative of (8^x/(7^x))	\frac{d}{dx}(\frac{8^{x}}{7^{x}})
integral of v/(v+2)	\int\:\frac{v}{v+2}dv
integral of (x^2)/(9+4x^2)	\int\:\frac{x^{2}}{9+4x^{2}}dx
integral of 3x^2sin(x^3-1)	\int\:3x^{2}\sin(x^{3}-1)dx
derivative of-4t(3t^5-1)^4	derivative\:-4t(3t^{5}-1)^{4}
derivative of ln(xsqrt(x^2-10))	\frac{d}{dx}(\ln(x\sqrt{x^{2}-10}))
tangent of f(x)=4x^2-3x+2	tangent\:f(x)=4x^{2}-3x+2
integral from 0 to 5 of x^2	\int\:_{0}^{5}x^{2}dx
derivative of y^{1-n}	\frac{d}{dx}(y^{1-n})
integral of-(x^3)/(3e^{x/2)}	\int\:-\frac{x^{3}}{3e^{\frac{x}{2}}}dx
d/(dq)(500q-(q^2)/(ln(q+300)))	\frac{d}{dq}(500q-\frac{q^{2}}{\ln(q+300)})
(\partial)/(\partial x)(tan(9+2x^2y^4z^2))	\frac{\partial\:}{\partial\:x}(\tan(9+2x^{2}y^{4}z^{2}))
derivative of (2-x^3)	\frac{d}{dx}((2-x)^{3})
area 1/8 x, 1/(x^2),x	area\:\frac{1}{8}x,\frac{1}{x^{2}},x
limit as x approaches infinity of ln(5x^2+12x-6)	\lim\:_{x\to\:\infty\:}(\ln(5x^{2}+12x-6))
integral of e^{9x}sin(x)	\int\:e^{9x}\sin(x)dx
integral from 2 to infinity of-3x^{-2}	\int\:_{2}^{\infty\:}-3x^{-2}dx
integral of 2x^2-x	\int\:2x^{2}-xdx
integral of (1+x)^{-4}	\int\:(1+x)^{-4}dx
(7du)/(dt)=u^2	\frac{7du}{dt}=u^{2}
4y^{''}+8y=0	4y^{\prime\:\prime\:}+8y=0
integral from-1 to 1 of x^{1/3}	\int\:_{-1}^{1}x^{\frac{1}{3}}dx
limit as x approaches-1 of sin(pix)	\lim\:_{x\to\:-1}(\sin(πx))
limit as x approaches 0+of (tan(3x))^x	\lim\:_{x\to\:0+}((\tan(3x))^{x})
area y=e^{5x},y=e^{6x},x=1	area\:y=e^{5x},y=e^{6x},x=1
derivative of sqrt(2xy)^3	\frac{d}{dx}(\sqrt{2xy}^{3})
area x^3-10x^2+16x,-x^3+10x^2-16x	area\:x^{3}-10x^{2}+16x,-x^{3}+10x^{2}-16x
sum from n=0 to infinity of 1/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{2^{n}}
derivative of (x^2-5x+3(4x^3+10x-5))	\frac{d}{dx}((x^{2}-5x+3)(4x^{3}+10x-5))
extreme f(x)=sqrt(x^2-11y^2)	extreme\:f(x)=\sqrt{x^{2}-11y^{2}}
derivative of f(x)=((e^{2x}-1))/x	derivative\:f(x)=\frac{(e^{2x}-1)}{x}
derivative of 2x+3y	derivative\:2x+3y
integral from-2 to-1 of (x^2-x-2)	\int\:_{-2}^{-1}(x^{2}-x-2)dx
f(x)=e^xln(x)	f(x)=e^{x}\ln(x)
limit as x approaches 0 of (sin(4x))/6	\lim\:_{x\to\:0}(\frac{\sin(4x)}{6})
(\partial)/(\partial y)(xe^{y^2}+yln(x))	\frac{\partial\:}{\partial\:y}(xe^{y^{2}}+y\ln(x))
integral of 6/((x-4)(x+2))	\int\:\frac{6}{(x-4)(x+2)}dx
y^{''}+81y=sec^2(9x)	y^{\prime\:\prime\:}+81y=\sec^{2}(9x)
slope of (1/4 , 7/8),(4 1/4 ,2 7/8)	slope\:(\frac{1}{4},\frac{7}{8}),(4\frac{1}{4},2\frac{7}{8})
sum from n=0 to infinity of 1/((2n+1)^6)	\sum\:_{n=0}^{\infty\:}\frac{1}{(2n+1)^{6}}
sqrt(y)dx+(1+x)dy=0	\sqrt{y}dx+(1+x)dy=0
(\partial)/(\partial x)((x^2+y^2-7)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{x^{2}+y^{2}-7}{xy})
(dx)/(dt)+3t^3x^5+x/t =0	\frac{dx}{dt}+3t^{3}x^{5}+\frac{x}{t}=0
derivative of x^2+8x-2	derivative\:x^{2}+8x-2
x^2dy+2xydx=0	x^{2}dy+2xydx=0
(d^2)/(dx^2)(-cos(x)ln(sec(x)+tan(x)))	\frac{d^{2}}{dx^{2}}(-\cos(x)\ln(\sec(x)+\tan(x)))
integral of (10)/(x^5)	\int\:\frac{10}{x^{5}}dx
ty^'+2y= 2/(1+t^2)	ty^{\prime\:}+2y=\frac{2}{1+t^{2}}
integral of \sqrt[3]{5-4x^2}(-8x)	\int\:\sqrt[3]{5-4x^{2}}(-8x)dx
y^{''}-3y^'+2y=e^xsin(2x)	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{x}\sin(2x)
(\partial)/(\partial x)(arctan(2xy))	\frac{\partial\:}{\partial\:x}(\arctan(2xy))
integral of ((e^x-e^{-x}))/(e^{2x)}	\int\:\frac{(e^{x}-e^{-x})}{e^{2x}}dx
(\partial)/(\partial s)(scos(t))	\frac{\partial\:}{\partial\:s}(s\cos(t))
derivative of sqrt(x^2-4)-2arcsec(x/2)	\frac{d}{dx}(\sqrt{x^{2}-4}-2\arcsec(\frac{x}{2}))
derivative of \sqrt[3]{6x+8}	\frac{d}{dx}(\sqrt[3]{6x+8})
limit as x approaches infinity of e^{5xln(1+1/x)}	\lim\:_{x\to\:\infty\:}(e^{5x\ln(1+\frac{1}{x})})
integral of (4x^3-5sqrt(x))/x	\int\:\frac{4x^{3}-5\sqrt{x}}{x}dx
(\partial)/(\partial x)(r/x)	\frac{\partial\:}{\partial\:x}(\frac{r}{x})
integral of 1/(x^2sqrt(64x^2+81))	\int\:\frac{1}{x^{2}\sqrt{64x^{2}+81}}dx
(dy)/(dx)=((x-1))/(y-4)	\frac{dy}{dx}=\frac{(x-1)}{y-4}
derivative of y= 1/2 x+8	derivative\:y=\frac{1}{2}x+8
f^'(x)=x	f^{\prime\:}(x)=x
derivative of ln(-e^{-x}+e+1)	\frac{d}{dx}(\ln(-e^{-x}+e+1))
derivative of x^4(x-2^2)	\frac{d}{dx}(x^{4}(x-2)^{2})
y^'=e^y5^x	y^{\prime\:}=e^{y}5^{x}
sum from n=1 to infinity of (60)/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{60}{6^{n}}
integral of e^{-0.08x}	\int\:e^{-0.08x}dx
derivative of tan^2(xcos(x))	\frac{d}{dx}(\tan^{2}(x)\cos(x))
sum from n=0 to infinity of 6(3/4)^n	\sum\:_{n=0}^{\infty\:}6(\frac{3}{4})^{n}
integral of (ln(11x))^2	\int\:(\ln(11x))^{2}dx
derivative of sqrt(3x+7)	derivative\:\sqrt{3x+7}
derivative of-2.25cos(1.5x)	derivative\:-2.25\cos(1.5x)
integral from 0 to 33 of (x-1)^{-1/5}	\int\:_{0}^{33}(x-1)^{-\frac{1}{5}}dx

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