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Popular Calculus Problems

taylor 1/(1-x),i	taylor\:\frac{1}{1-x},i
area y=x^3,y=x^2-4x,[-1,1]	area\:y=x^{3},y=x^{2}-4x,[-1,1]
integral from 1 to 4 of (7x+sqrt(x))	\int\:_{1}^{4}(7x+\sqrt{x})dx
integral of (3x^2-4x+2)	\int\:(3x^{2}-4x+2)dx
integral of 2/(sqrt(t))	\int\:\frac{2}{\sqrt{t}}dt
sum from n=0 to infinity of-n	\sum\:_{n=0}^{\infty\:}-n
y^'=3sin(x)(2-y)	y^{\prime\:}=3\sin(x)(2-y)
derivative of (-14/(sqrt(x)))	\frac{d}{dx}(\frac{-14}{\sqrt{x}})
derivative of x-1	derivative\:x-1
limit as x approaches infinity of 1+5/x	\lim\:_{x\to\:\infty\:}(1+\frac{5}{x})
integral of 3/(4-x)	\int\:\frac{3}{4-x}dx
y^'-3y=te^{2t}	y^{\prime\:}-3y=te^{2t}
integral from 0 to pi/2 of 19sin^2(2x)	\int\:_{0}^{\frac{π}{2}}19\sin^{2}(2x)dx
derivative of 5sin(1/5 x)	derivative\:5\sin(\frac{1}{5}x)
limit as x approaches 4 of (x-4)/(x+4)	\lim\:_{x\to\:4}(\frac{x-4}{x+4})
derivative of-1/((2-x^2))	\frac{d}{dx}(-\frac{1}{(2-x)^{2}})
(\partial)/(\partial x)(3x^2+y^3)	\frac{\partial\:}{\partial\:x}(3x^{2}+y^{3})
derivative of y=x^{2/5}	derivative\:y=x^{\frac{2}{5}}
derivative of ({f}(x,h(x+h)-{f}(x))/h)	\frac{d}{dx}(\frac{{f}(x,h)(x+h)-{f}(x)}{h})
d/(dn)(i^n)	\frac{d}{dn}(i^{n})
limit as x approaches 1 of (x^3)/3	\lim\:_{x\to\:1}(\frac{x^{3}}{3})
derivative of f(x)=(sqrt(x))/(5+x)	derivative\:f(x)=\frac{\sqrt{x}}{5+x}
tangent of f(x)=(sqrt(x))/(x+1),\at x=4	tangent\:f(x)=\frac{\sqrt{x}}{x+1},\at\:x=4
laplacetransform 2s	laplacetransform\:2s
2xdy+(x^2y^4+1)ydx=0	2xdy+(x^{2}y^{4}+1)ydx=0
integral of 2cos(nx)	\int\:2\cos(nx)dx
derivative of ((x^2+4)/(x^2-4))^2	derivative\:(\frac{x^{2}+4}{x^{2}-4})^{2}
limit as x approaches 5-of 6/(x-5)	\lim\:_{x\to\:5-}(\frac{6}{x-5})
integral of ln(x+7)	\int\:\ln(x+7)dx
integral of 3(ln(x))^2	\int\:3(\ln(x))^{2}dx
integral of x(x-3)	\int\:x(x-3)dx
derivative of (cos(x^3)^2)	\frac{d}{dx}((\cos(x^{3}))^{2})
2xy+x^3=(xdy)/(dx)	2xy+x^{3}=\frac{xdy}{dx}
integral of (sin(3t+10))/(cos^2(3t+10))	\int\:\frac{\sin(3t+10)}{\cos^{2}(3t+10)}dt
derivative of 2sqrt(x)ln(x)	\frac{d}{dx}(2\sqrt{x}\ln(x))
tangent of (x-y-1)^3=x,(1,-1)	tangent\:(x-y-1)^{3}=x,(1,-1)
y^{''}+y^'=3sin(4x)	y^{\prime\:\prime\:}+y^{\prime\:}=3\sin(4x)
limit as n approaches infinity of (n!)^n	\lim\:_{n\to\:\infty\:}((n!)^{n})
integral of ((2x+7)/(x^2+2x+5))	\int\:(\frac{2x+7}{x^{2}+2x+5})dx
tangent of (3x)/((x+1)^2)(0)	tangent\:\frac{3x}{(x+1)^{2}}(0)
6x+y^{''}=0	6x+y^{\prime\:\prime\:}=0
derivative of (x^4-sec(4x^2-2))^{-4}	derivative\:(x^{4}-\sec(4x^{2}-2))^{-4}
(\partial)/(\partial x)(y/(x^2))	\frac{\partial\:}{\partial\:x}(\frac{y}{x^{2}})
integral from 0 to 10 of te^{-0.6t}	\int\:_{0}^{10}te^{-0.6t}dt
x^'=rx-12	x^{\prime\:}=rx-12
6y^{''}+9y^'-y=23	6y^{\prime\:\prime\:}+9y^{\prime\:}-y=23
derivative of sqrt(ycos(x))	\frac{d}{dx}(\sqrt{y\cos(x)})
inverse oflaplace 1/(1-s)	inverselaplace\:\frac{1}{1-s}
derivative of y=(cos(x))/(sin(x))	derivative\:y=\frac{\cos(x)}{\sin(x)}
limit as x approaches 5 of (x-6)/(x-5)	\lim\:_{x\to\:5}(\frac{x-6}{x-5})
integral of cos(6x)-cos(-6x)	\int\:\cos(6x)-\cos(-6x)dx
integral of (cos(θ)-cos(2θ))/(1-cos(θ))	\int\:\frac{\cos(θ)-\cos(2θ)}{1-\cos(θ)}dθ
derivative of x(ln(x))	derivative\:x(\ln(x))
(\partial)/(\partial x)(x+y-8)	\frac{\partial\:}{\partial\:x}(x+y-8)
derivative of f(x)=(x^2+5)(8-x)	derivative\:f(x)=(x^{2}+5)(8-x)
limit as x approaches 1 of sqrt(4x^2+2)	\lim\:_{x\to\:1}(\sqrt{4x^{2}+2})
derivative of 4/(sqrt(x))-1	derivative\:\frac{4}{\sqrt{x}}-1
integral of xe^{(-x^2)/2}	\int\:xe^{\frac{-x^{2}}{2}}dx
integral from-2 to 6 of sqrt(12+4x-x^2)	\int\:_{-2}^{6}\sqrt{12+4x-x^{2}}dx
integral of t^5cos(2t^6)	\int\:t^{5}\cos(2t^{6})dt
y^{''}-3y^'+2y=e^x	y^{\prime\:\prime\:}-3y^{\prime\:}+2y=e^{x}
derivative of 1+sin(2x)	\frac{d}{dx}(1+\sin(2x))
integral of 7sin^2(x)	\int\:7\sin^{2}(x)dx
derivative of x^{15x}	\frac{d}{dx}(x^{15x})
integral of (6x)/((x-5)^2)	\int\:\frac{6x}{(x-5)^{2}}dx
limit as x approaches 2 of sqrt(6x^2+1)	\lim\:_{x\to\:2}(\sqrt{6x^{2}+1})
integral from-infinity to 0 of e^{9x}	\int\:_{-\infty\:}^{0}e^{9x}dx
t^2((dy)/(dt))+4ty-y^3=0	t^{2}(\frac{dy}{dt})+4ty-y^{3}=0
slope of x^3+y^3-6xy=0,(4/3 , 8/3)	slope\:x^{3}+y^{3}-6xy=0,(\frac{4}{3},\frac{8}{3})
integral from 2 to 5 of 4x^3	\int\:_{2}^{5}4x^{3}dx
derivative of f(x)=(1-x^2)/((1+x^2)^2)	derivative\:f(x)=\frac{1-x^{2}}{(1+x^{2})^{2}}
limit as x approaches c of \sqrt[3]{27}	\lim\:_{x\to\:c}(\sqrt[3]{27})
integral from-infinity to-1 of e^{-16t}	\int\:_{-\infty\:}^{-1}e^{-16t}dt
integral of x^{-1/2}ln(x)	\int\:x^{-\frac{1}{2}}\ln(x)dx
integral from-pi/3 to 0 of 6sec^3(x)	\int\:_{-\frac{π}{3}}^{0}6\sec^{3}(x)dx
integral of x^2ye^{xy}	\int\:x^{2}ye^{xy}dx
(y-x3)dx+(x+y3)dy=0	(y-x3)dx+(x+y3)dy=0
f^'(x)=xe^{x^2}	f^{\prime\:}(x)=xe^{x^{2}}
(\partial)/(\partial x)(x+6y)	\frac{\partial\:}{\partial\:x}(x+6y)
integral of 4e^7	\int\:4e^{7}dx
integral of 6x^4e^{-x}	\int\:6x^{4}e^{-x}dx
tangent of f(x)=x^3+x^2+6/x ,\at x=1	tangent\:f(x)=x^{3}+x^{2}+\frac{6}{x},\at\:x=1
slope of (-4,6),(10,-1)	slope\:(-4,6),(10,-1)
y^'=((x^2e^{y/x}+y^2))/(xy)	y^{\prime\:}=\frac{(x^{2}e^{\frac{y}{x}}+y^{2})}{xy}
(\partial)/(\partial x)(2xy+sin(x))	\frac{\partial\:}{\partial\:x}(2xy+\sin(x))
inverse oflaplace ((e^{-s}))/(s(s+1))	inverselaplace\:\frac{(e^{-s})}{s(s+1)}
derivative of 128sin(2x)	\frac{d}{dx}(128\sin(2x))
y=(x^2+4)^2	y=(x^{2}+4)^{2}
area x^2,0,-1,2	area\:x^{2},0,-1,2
derivative of sin(pix^2)	\frac{d}{dx}(\sin(πx^{2}))
limit as x approaches 0+of 1/(xln(x^9))	\lim\:_{x\to\:0+}(\frac{1}{x\ln(x^{9})})
y^'=-y/(x^2)+1/(x^2y^2)	y^{\prime\:}=-\frac{y}{x^{2}}+\frac{1}{x^{2}y^{2}}
limit as x approaches 6+of 1/((x-6)^2)	\lim\:_{x\to\:6+}(\frac{1}{(x-6)^{2}})
derivative of (3^{x^2}+x/(2^{x^2)})	\frac{d}{dx}(\frac{3^{x^{2}}+x}{2^{x^{2}}})
integral of (2(csc(x))^2)/(cot(x))	\int\:\frac{2(\csc(x))^{2}}{\cot(x)}dx
integral from 0 to 3 of 3e^x	\int\:_{0}^{3}3e^{x}dx
integral of 6/((9x^2+1)^2)	\int\:\frac{6}{(9x^{2}+1)^{2}}dx
derivative of y=(arctan(2x))/x	derivative\:y=\frac{\arctan(2x)}{x}
limit as x approaches 0 of (x+1)^{ln(x)}	\lim\:_{x\to\:0}((x+1)^{\ln(x)})
derivative of f(x)=9+5x^2-2x^3	derivative\:f(x)=9+5x^{2}-2x^{3}

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