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Popular Calculus Problems

tangent of f(x)=x^2+8,\at x=2	tangent\:f(x)=x^{2}+8,\at\:x=2
integral of e^x+2	\int\:e^{x}+2dx
limit as x approaches-infinity of x^2+6	\lim\:_{x\to\:-\infty\:}(x^{2}+6)
derivative of (x^4+3x^2-2^5)	\frac{d}{dx}((x^{4}+3x^{2}-2)^{5})
integral of ((3y-8))/(y^2-4y-5)	\int\:\frac{(3y-8)}{y^{2}-4y-5}dy
integral of 1/((3x+7)^2)	\int\:\frac{1}{(3x+7)^{2}}dx
inverse oflaplace (s^2)/(s-1)	inverselaplace\:\frac{s^{2}}{s-1}
taylor e^{-13x}	taylor\:e^{-13x}
(dy)/(dx)=((x^2-3y^2))/(2xy)	\frac{dy}{dx}=\frac{(x^{2}-3y^{2})}{2xy}
(\partial)/(\partial x)((4s+t)/(3s-5t))	\frac{\partial\:}{\partial\:x}(\frac{4s+t}{3s-5t})
y^{''}+49y=0,y(0)=4,y^{''}(0)=6	y^{\prime\:\prime\:}+49y=0,y(0)=4,y^{\prime\:\prime\:}(0)=6
integral from 0 to 1 of xsin(x)	\int\:_{0}^{1}x\sin(x)dx
limit as x approaches-1 of (2x+8)/x	\lim\:_{x\to\:-1}(\frac{2x+8}{x})
derivative of 60e^{-4.8x}sin(16x)	\frac{d}{dx}(60e^{-4.8x}\sin(16x))
area x=y^2,x=9	area\:x=y^{2},x=9
integral of e^{-cx^2}	\int\:e^{-cx^{2}}dx
integral of (x^2)/((x^2-8^2)^{3/2)}	\int\:\frac{x^{2}}{(x^{2}-8^{2})^{\frac{3}{2}}}dx
(\partial)/(\partial x)(1+xy^2-2z^2)	\frac{\partial\:}{\partial\:x}(1+xy^{2}-2z^{2})
integral of (e^x)/(e^x)	\int\:\frac{e^{x}}{e^{x}}dx
derivative of 1/(y^2)-9/(y^4)(y+3y^3)	derivative\:\frac{1}{y^{2}}-\frac{9}{y^{4}}(y+3y^{3})
sum from n=1 to infinity of (10n)/(n+1)	\sum\:_{n=1}^{\infty\:}\frac{10n}{n+1}
derivative of 1/((-3x^2+3x-2^3))	\frac{d}{dx}(\frac{1}{(-3x^{2}+3x-2)^{3}})
integral of-2x^3(-5x^2-x+12)	\int\:-2x^{3}(-5x^{2}-x+12)dx
(\partial)/(\partial z)(-2e^xcos(yz))	\frac{\partial\:}{\partial\:z}(-2e^{x}\cos(yz))
integral of x^3(1+x^4)^3	\int\:x^{3}(1+x^{4})^{3}dx
derivative of sin(x+2)	\frac{d}{dx}(\sin(x+2))
integral from-infinity to 0 of 1/(4-3x)	\int\:_{-\infty\:}^{0}\frac{1}{4-3x}dx
inverse oflaplace s/((s-3)^3)	inverselaplace\:\frac{s}{(s-3)^{3}}
(\partial)/(\partial y)(ln(2x^2+3y^2))	\frac{\partial\:}{\partial\:y}(\ln(2x^{2}+3y^{2}))
derivative of A/(x^9+Be^x)	\frac{d}{dx}(\frac{A}{x^{9}}+Be^{x})
(4+x)y^'=8y	(4+x)y^{\prime\:}=8y
integral of (x^2-7x+2)	\int\:(x^{2}-7x+2)dx
tangent of y=e^{5x},\at x= 1/5 ln(5)	tangent\:y=e^{5x},\at\:x=\frac{1}{5}\ln(5)
integral of 5sin^3(xco)s^7x	\int\:5\sin^{3}(xco)s^{7}xdx
derivative of arccsc(4x^2+1)	\frac{d}{dx}(\arccsc(4x^{2}+1))
integral of (5x^4+x/7)	\int\:(5x^{4}+\frac{x}{7})dx
(dy)/(dx)+y+2cos(x)=0	\frac{dy}{dx}+y+2\cos(x)=0
derivative of ((x^2+3)/x)	\frac{d}{dx}(\frac{(x^{2}+3)}{x})
inverse oflaplace s/(s^2+9)	inverselaplace\:\frac{s}{s^{2}+9}
derivative of (2x-9/(sqrt(x)))	\frac{d}{dx}(\frac{2x-9}{\sqrt{x}})
integral of 3x^3e^{-x^2}	\int\:3x^{3}e^{-x^{2}}dx
derivative of y= 1/(7t+3)	derivative\:y=\frac{1}{7t+3}
integral from 0 to 15 of x/(sqrt(x+1))	\int\:_{0}^{15}\frac{x}{\sqrt{x+1}}dx
area-x^3+3,y=x,x=-1,x=1	area\:-x^{3}+3,y=x,x=-1,x=1
integral of (xcos(x)+sin(x))sqrt(1+u)	\int\:(x\cos(x)+\sin(x))\sqrt{1+u}dx
integral of x^3-4x+2	\int\:x^{3}-4x+2dx
(dr)/(dθ)=-pisin(piθ),r(2)=3	\frac{dr}{dθ}=-π\sin(πθ),r(2)=3
derivative of log_{7}(3x^2+1)	\frac{d}{dx}(\log_{7}(3x^{2}+1))
derivative of sqrt(5+x^2)	derivative\:\sqrt{5+x^{2}}
integral of e^{-st}sin(3t)	\int\:e^{-st}\sin(3t)dt
limit as t approaches 0 of sin^t(t)	\lim\:_{t\to\:0}(\sin^{t}(t))
derivative of y=sin((pix)^4)	derivative\:y=\sin((πx)^{4})
(\partial)/(\partial x)(x^3-7x^2+y^3-5y)	\frac{\partial\:}{\partial\:x}(x^{3}-7x^{2}+y^{3}-5y)
derivative of sqrt(5+\sqrt{3x)}	derivative\:\sqrt{5+\sqrt{3x}}
limit as x approaches 0-of (ln(x))/x	\lim\:_{x\to\:0-}(\frac{\ln(x)}{x})
integral of 7tan(x)sec^3(x)	\int\:7\tan(x)\sec^{3}(x)dx
integral from 0 to 6 of (6x^2-1)	\int\:_{0}^{6}(6x^{2}-1)dx
taylor 2xln(1+(x^2)/4)	taylor\:2x\ln(1+\frac{x^{2}}{4})
integral of csc^2(2x)cot(2x)	\int\:\csc^{2}(2x)\cot(2x)dx
sum from n=0 to infinity of 1/(e^n)	\sum\:_{n=0}^{\infty\:}\frac{1}{e^{n}}
derivative of (sqrt(x)+1/(sqrt(x)+4))	\frac{d}{dx}(\frac{\sqrt{x}+1}{\sqrt{x}+4})
(\partial)/(\partial x)(tan(x^3+y^2))	\frac{\partial\:}{\partial\:x}(\tan(x^{3}+y^{2}))
integral of 2/(2x^2+3x+1)	\int\:\frac{2}{2x^{2}+3x+1}dx
limit as x approaches 3+of (x+3)/(x-3)	\lim\:_{x\to\:3+}(\frac{x+3}{x-3})
(\partial)/(\partial x)(x/(x^6-y^7))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{6}-y^{7}})
sum from n=4 to infinity of (x+1)^n	\sum\:_{n=4}^{\infty\:}(x+1)^{n}
derivative of f(x)=x^{-8}	derivative\:f(x)=x^{-8}
y^'=-2y+t,y(0)=-5	y^{\prime\:}=-2y+t,y(0)=-5
integral of 1/(y^2-3y+2)	\int\:\frac{1}{y^{2}-3y+2}dy
integral of (x^2+3x+1)	\int\:(x^{2}+3x+1)dx
(dy)/(dx)+(x^2-1)y=-xy^6	\frac{dy}{dx}+(x^{2}-1)y=-xy^{6}
integral of 0.03e^{-0.03x}	\int\:0.03e^{-0.03x}dx
(\partial)/(\partial y)(arctan(yz))	\frac{\partial\:}{\partial\:y}(\arctan(yz))
e^{-x}(y^'-y)=y^2	e^{-x}(y^{\prime\:}-y)=y^{2}
limit as x approaches infinity of (ln(1+e^{-x}))/(e^{-x)}	\lim\:_{x\to\:\infty\:}(\frac{\ln(1+e^{-x})}{e^{-x}})
limit as x approaches-1 of 3(2x-1)^2	\lim\:_{x\to\:-1}(3(2x-1)^{2})
integral of (3sin(x)+2sec(x))/(tan(x))	\int\:\frac{3\sin(x)+2\sec(x)}{\tan(x)}dx
derivative of-5/(x^6)	derivative\:-\frac{5}{x^{6}}
derivative of ln(2^x)	derivative\:\ln(2^{x})
integral of (t^2)/(1+t^2)	\int\:\frac{t^{2}}{1+t^{2}}dt
integral of 8x^3+1/x	\int\:8x^{3}+\frac{1}{x}dx
(\partial)/(\partial y)(e^{7xe^y})	\frac{\partial\:}{\partial\:y}(e^{7xe^{y}})
derivative of f(x)=6x^3cot(x)	derivative\:f(x)=6x^{3}\cot(x)
tangent of f(x)=x^3sqrt(5-x^2),\at x=2	tangent\:f(x)=x^{3}\sqrt{5-x^{2}},\at\:x=2
derivative of-1/2 e^{-x^2}	\frac{d}{dx}(-\frac{1}{2}e^{-x^{2}})
(\partial)/(\partial x)(sqrt(x^3+sin(3y)))	\frac{\partial\:}{\partial\:x}(\sqrt{x^{3}+\sin(3y)})
integral of 1/(sqrt(x^2+c))	\int\:\frac{1}{\sqrt{x^{2}+c}}dx
inverse oflaplace 2/((s-4)^3)	inverselaplace\:\frac{2}{(s-4)^{3}}
integral from-pi to pi of sin(kx)cos(nx)	\int\:_{-π}^{π}\sin(kx)\cos(nx)dx
x^'=ax-bx^2	x^{\prime\:}=ax-bx^{2}
limit as x approaches-1 of (f(x))/(x+1)	\lim\:_{x\to\:-1}(\frac{f(x)}{x+1})
y^'=(-xy^2)/2	y^{\prime\:}=\frac{-xy^{2}}{2}
integral of 1/N	\int\:\frac{1}{N}dN
integral of (1/(y^2))	\int\:(\frac{1}{y^{2}})dy
integral of e^xsin(t-x)	\int\:e^{x}\sin(t-x)dx
derivative of x^{5/4}+e^{-3x}	\frac{d}{dx}(x^{\frac{5}{4}}+e^{-3x})
limit as x approaches-2 of [-6]^2	\lim\:_{x\to\:-2}([-6]^{2})
y^'=9x^2e^{-y},y(0)=1	y^{\prime\:}=9x^{2}e^{-y},y(0)=1
integral of 4x(x-2)^3	\int\:4x(x-2)^{3}dx
sum from n=1 to infinity of n/(6^n)	\sum\:_{n=1}^{\infty\:}\frac{n}{6^{n}}

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