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Popular Calculus Problems

integral from 0 to 2 of 1/(1+e^{2x)}	\int\:_{0}^{2}\frac{1}{1+e^{2x}}dx
limit as x approaches-infinity of-5x^3	\lim\:_{x\to\:-\infty\:}(-5x^{3})
integral of (3x^3+4x)/((x^2+5)^2)	\int\:\frac{3x^{3}+4x}{(x^{2}+5)^{2}}dx
integral of (3x^4-2x+5)/(x+1)	\int\:\frac{3x^{4}-2x+5}{x+1}dx
derivative of Ax	\frac{d}{dx}(Ax)
d/(dy)(1-xycos(piy))	\frac{d}{dy}(1-xy\cos(πy))
derivative of (x^2)/(40)	derivative\:\frac{x^{2}}{40}
xy^'=e^x-y	xy^{\prime\:}=e^{x}-y
laplacetransform f(t)= 1/20 t^5e^{2t}	laplacetransform\:f(t)=\frac{1}{20}t^{5}e^{2t}
limit as x approaches 0 of (x)^2	\lim\:_{x\to\:0}((x)^{2})
integral of 1/(6x^2+36x+78)	\int\:\frac{1}{6x^{2}+36x+78}dx
tan(x)sin(y)dx+cos(x)cot(y)dy=0	\tan(x)\sin(y)dx+\cos(x)\cot(y)dy=0
integral of (2x^2-x+4)/(x(x^2+4))	\int\:\frac{2x^{2}-x+4}{x(x^{2}+4)}dx
y^{''}-2y^'+y=te^t,y(0)=1,y^'(0)=1	y^{\prime\:\prime\:}-2y^{\prime\:}+y=te^{t},y(0)=1,y^{\prime\:}(0)=1
integral of (20)/x	\int\:\frac{20}{x}dx
limit as x approaches 0 of 5+2e^{(-5)/x}	\lim\:_{x\to\:0}(5+2e^{\frac{-5}{x}})
integral of cos^2(wx)	\int\:\cos^{2}(wx)dx
tangent of f(x)=3sec(x),\at x= pi/6	tangent\:f(x)=3\sec(x),\at\:x=\frac{π}{6}
integral of 1/(7x-1)	\int\:\frac{1}{7x-1}dx
limit as x approaches 0 of (sin(x/4))/x	\lim\:_{x\to\:0}(\frac{\sin(\frac{x}{4})}{x})
integral of cos^3(x)tan^2(x)	\int\:\cos^{3}(x)\tan^{2}(x)dx
derivative of y=(3\sqrt[3]{x})/(1-x)	\frac{d}{dx}y=\frac{3\sqrt[3]{x}}{1-x}
tangent of f(x)= 4/(1+x^2),\at x=1	tangent\:f(x)=\frac{4}{1+x^{2}},\at\:x=1
limit as x approaches pi/2-of e^{sec(x)}	\lim\:_{x\to\:\frac{π}{2}-}(e^{\sec(x)})
integral of (esqrt(t))/(sqrt(t))	\int\:\frac{e\sqrt{t}}{\sqrt{t}}dt
integral of (x^2)/(4+x^2)	\int\:\frac{x^{2}}{4+x^{2}}dx
(\partial)/(\partial x)(ycos(pix^2y))	\frac{\partial\:}{\partial\:x}(y\cos(πx^{2}y))
f(x)=cos(e^x)	f(x)=\cos(e^{x})
limit as x approaches-2 of 3/2	\lim\:_{x\to\:-2}(\frac{3}{2})
(dy}{dx}=0.1ln(\frac{3000)/y)y	\frac{dy}{dx}=0.1\ln(\frac{3000}{y})y
(\partial)/(\partial x)(2x^2*4x^3)	\frac{\partial\:}{\partial\:x}(2x^{2}\cdot\:4x^{3})
integral from-1 to 1 of sqrt(x^2+1)	\int\:_{-1}^{1}\sqrt{x^{2}+1}dx
(sin(t))y^'+(cos(t))y=3t(sin(t))	(\sin(t))y^{\prime\:}+(\cos(t))y=3t(\sin(t))
derivative of f(x)=(4x+2)/(4x-2)	derivative\:f(x)=\frac{4x+2}{4x-2}
derivative of arctan(t)	derivative\:\arctan(t)
limit as x approaches-1 of (x+2)^2	\lim\:_{x\to\:-1}((x+2)^{2})
derivative of sin^2(x)cos^2(x)	derivative\:\sin^{2}(x)\cos^{2}(x)
integral of xe^3x	\int\:xe^{3}xdx
derivative of f(x)=(8x+9)(x^3-6)	derivative\:f(x)=(8x+9)(x^{3}-6)
derivative of-64cos(2x)	derivative\:-64\cos(2x)
derivative of 3x(2x-1)^3	derivative\:3x(2x-1)^{3}
derivative of 1-sec(x)	\frac{d}{dx}(1-\sec(x))
integral of (x^{1.5}+9x^{3.5})	\int\:(x^{1.5}+9x^{3.5})dx
(7x+2y)(dy)/(dx)=-2x-7y	(7x+2y)\frac{dy}{dx}=-2x-7y
limit as x approaches 2+of (x+4)/(x-2)	\lim\:_{x\to\:2+}(\frac{x+4}{x-2})
limit as x approaches 0 of (7x)/(\|x\|)	\lim\:_{x\to\:0}(\frac{7x}{\left\|x\right\|})
limit as x approaches 1-of ln(x^2-1)	\lim\:_{x\to\:1-}(\ln(x^{2}-1))
limit as x approaches 6+of 7/(x-6)	\lim\:_{x\to\:6+}(\frac{7}{x-6})
integral from 0 to 7 of 2t^2-20t+48	\int\:_{0}^{7}2t^{2}-20t+48dt
integral of tan^3(15pix)	\int\:\tan^{3}(15πx)dx
integral from 1 to 4 of 4/x-(16)/(x^2)	\int\:_{1}^{4}\frac{4}{x}-\frac{16}{x^{2}}dx
integral of cos(x/a)sin(x/a)	\int\:\cos(\frac{x}{a})\sin(\frac{x}{a})dx
derivative of (2^x/(1-x^2))	\frac{d}{dx}(\frac{2^{x}}{1-x^{2}})
integral of 1/(x+!)	\int\:\frac{1}{x+!}dx
derivative of (2x-1(3x+4)(x+7))	\frac{d}{dx}((2x-1)(3x+4)(x+7))
derivative of (y^2-3x^2/(y^4))	\frac{d}{dx}(\frac{y^{2}-3x^{2}}{y^{4}})
(\partial)/(\partial x)(+6-5+6x)	\frac{\partial\:}{\partial\:x}(+6-5+6x)
sum from n=0 to infinity of 2/(7^n)	\sum\:_{n=0}^{\infty\:}\frac{2}{7^{n}}
limit as x approaches 2-of arcsin(x-1)	\lim\:_{x\to\:2-}(\arcsin(x-1))
limit as x approaches pi of 1/(x-pi)	\lim\:_{x\to\:π}(\frac{1}{x-π})
integral of 1/(\sqrt[5]{x^2)}	\int\:\frac{1}{\sqrt[5]{x^{2}}}dx
derivative of f(x)=(6x+1)^2	derivative\:f(x)=(6x+1)^{2}
derivative of sqrt(ln(8x))	\frac{d}{dx}(\sqrt{\ln(8x)})
2xy*y^'=-(x^2+y^2)	2\cdot\:x\cdot\:y\cdot\:y^{\prime\:}=-(x^{2}+y^{2})
derivative of (x^2/((x^2+5)^3))	\frac{d}{dx}(\frac{x^{2}}{(x^{2}+5)^{3}})
tangent of 9y^7+4x^3=8y+5x,(1,1)	tangent\:9y^{7}+4x^{3}=8y+5x,(1,1)
(\partial)/(\partial x)(cos^5(x^7y^5))	\frac{\partial\:}{\partial\:x}(\cos^{5}(x^{7}y^{5}))
xy^'+(1-x)y=0	xy^{\prime\:}+(1-x)y=0
(dN)/(dt)=N(1-0.0005N)	\frac{dN}{dt}=N(1-0.0005N)
x(dy)/(dx)+y=(xy)^{3/2}	x\frac{dy}{dx}+y=(xy)^{\frac{3}{2}}
derivative of sqrt(y-x)n(y+x)	\frac{d}{dx}(\sqrt{y-x}n(y+x))
(\partial)/(\partial y)(x-y-1)	\frac{\partial\:}{\partial\:y}(x-y-1)
limit as x approaches 0 of e^{-x}cos(x)	\lim\:_{x\to\:0}(e^{-x}\cos(x))
(d^2)/(dx^2)(sec(x))	\frac{d^{2}}{dx^{2}}(\sec(x))
limit as e^{e^x} approaches 0+of (e^{e^x-2})/(e^{e^x)}	\lim\:_{e^{e^{x}}\to\:0+}(\frac{e^{e^{x}-2}}{e^{e^{x}}})
derivative of (x-1)(x^2-8x+7)	derivative\:(x-1)(x^{2}-8x+7)
derivative of sin^2(x+x)	\frac{d}{dx}(\sin^{2}(x)+x)
derivative of 5x^3cos(x)	\frac{d}{dx}(5x^{3}\cos(x))
(\partial)/(\partial x)(sqrt(yx))	\frac{\partial\:}{\partial\:x}(\sqrt{yx})
(\partial)/(\partial x)(3y)	\frac{\partial\:}{\partial\:x}(3y)
integral of 9/x	\int\:\frac{9}{x}dx
derivative of xln(2)	\frac{d}{dx}(x\ln(2))
(\partial)/(\partial x)(xyz-tan(x+y+z))	\frac{\partial\:}{\partial\:x}(xyz-\tan(x+y+z))
sum from n=1 to infinity of 2/(n^2-1)	\sum\:_{n=1}^{\infty\:}\frac{2}{n^{2}-1}
5y^{''}+40y^'+80y=0	5y^{\prime\:\prime\:}+40y^{\prime\:}+80y=0
limit as x approaches 9 of 5x+3	\lim\:_{x\to\:9}(5x+3)
integral of x	\int\:xdx
y^'+2y=4t	y^{\prime\:}+2y=4t
(\partial)/(\partial y)(4x^{3y})	\frac{\partial\:}{\partial\:y}(4x^{3y})
3y^'+4y=e^{-x}	3y^{\prime\:}+4y=e^{-x}
parity tan(5-sin(2t))	parity\:\tan(5-\sin(2t))
(dy)/(dx)+3x^2y=2xe^{-x^3}	\frac{dy}{dx}+3x^{2}y=2xe^{-x^{3}}
y^'+2x^{-1}y=x^{-1}sin(2x)	y^{\prime\:}+2x^{-1}y=x^{-1}\sin(2x)
integral from-2 to 1 of x(4-x^2)-(x+2)	\int\:_{-2}^{1}x(4-x^{2})-(x+2)dx
integral of 1/(2^x+3)	\int\:\frac{1}{2^{x}+3}dx
sum from n=1 to infinity of 1/(n(n+5))	\sum\:_{n=1}^{\infty\:}\frac{1}{n(n+5)}
sum from n=0 to infinity of (i^n)/(3^n)	\sum\:_{n=0}^{\infty\:}\frac{i^{n}}{3^{n}}
implicit (ex)/y =9x-y	implicit\:\frac{ex}{y}=9x-y
integral of (17)/(x^3-125)	\int\:\frac{17}{x^{3}-125}dx
slope of (-2,-3),(6,2)	slope\:(-2,-3),(6,2)

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