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Popular Calculus Problems

integral from 0 to N of e^{-st}cos(5t)	\int\:_{0}^{N}e^{-st}\cos(5t)dt
integral of 4/((x-6)^3)	\int\:\frac{4}{(x-6)^{3}}dx
100x+(dy)/(dx)=xy	100x+\frac{dy}{dx}=xy
limit as t approaches 10 of (t^2+3t-130)/(t^2-100)	\lim\:_{t\to\:10}(\frac{t^{2}+3t-130}{t^{2}-100})
y^'+2x=0	y^{\prime\:}+2x=0
integral of (1+2x)^2	\int\:(1+2x)^{2}dx
derivative of (-3x-2)/(2x^2+x+3)	derivative\:\frac{-3x-2}{2x^{2}+x+3}
derivative of (e^x/(x^3))	\frac{d}{dx}(\frac{e^{x}}{x^{3}})
(\partial)/(\partial y)(-2xe^{xy})	\frac{\partial\:}{\partial\:y}(-2xe^{xy})
y^'=(x-14)^2	y^{\prime\:}=(x-14)^{2}
y^{''}+324y=sec(18x),y(0)=2,y^'(0)=-1	y^{\prime\:\prime\:}+324y=\sec(18x),y(0)=2,y^{\prime\:}(0)=-1
sum from n=3 to infinity of 3/(n^2-3n+2)	\sum\:_{n=3}^{\infty\:}\frac{3}{n^{2}-3n+2}
limit as x approaches 0 of ((1+x)^2)/x	\lim\:_{x\to\:0}(\frac{(1+x)^{2}}{x})
integral of ((ln(x))^2+1)/(ln(x))	\int\:\frac{(\ln(x))^{2}+1}{\ln(x)}dx
y^'=(e^{x-y})/(e^x+1)	y^{\prime\:}=\frac{e^{x-y}}{e^{x}+1}
(d^2y)/(dx^2)-5(dy)/(dx)+ky=0	\frac{d^{2}y}{dx^{2}}-5\frac{dy}{dx}+ky=0
sum from n=1 to infinity of (3^n)/(n2^n)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{n2^{n}}
(\partial)/(\partial y)(arctan(y/x))	\frac{\partial\:}{\partial\:y}(\arctan(\frac{y}{x}))
y^{''}+18y^'+97y=0	y^{\prime\:\prime\:}+18y^{\prime\:}+97y=0
(\partial)/(\partial x)(arcsin(y/((x^2+y^2)^{1/2)}))	\frac{\partial\:}{\partial\:x}(\arcsin(\frac{y}{(x^{2}+y^{2})^{\frac{1}{2}}}))
integral of tan(x)-2sin(x)	\int\:\tan(x)-2\sin(x)dx
derivative of (300/x)	\frac{d}{dx}(\frac{300}{x})
(\partial)/(\partial x)(xyz)	\frac{\partial\:}{\partial\:x}(xyz)
simplify f(x)g(x)h(x)	simplify\:f(x)g(x)h(x)
derivative of ((\sqrt[3]{t}))/(t-3)	derivative\:\frac{(\sqrt[3]{t})}{t-3}
integral of-1/2	\int\:-\frac{1}{2}dx
integral from 0 to 1 of sqrt(x-x^2)	\int\:_{0}^{1}\sqrt{x-x^{2}}dx
integral of (y-1)(2y+1)	\int\:(y-1)(2y+1)dy
(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 (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
limit as x approaches-1 of sin(pix)	\lim\:_{x\to\:-1}(\sin(πx))
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
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 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
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))

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