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Popular Calculus Problems

(1+x^2)(dy)/(dx)-(2xy+x^2+x^4)=0	(1+x^{2})\frac{dy}{dx}-(2xy+x^{2}+x^{4})=0
(dx)/(dt)-2/(3t)x=4tx^{-5}	\frac{dx}{dt}-\frac{2}{3t}x=4tx^{-5}
derivative of x^2(e^x-1)	\frac{d}{dx}(x^{2}(e^{x}-1))
limit as x approaches pi/2 of 2sec(x)	\lim\:_{x\to\:\frac{π}{2}}(2\sec(x))
integral from 1 to 2 of 3(ln(x))/(x^2)	\int\:_{1}^{2}3\frac{\ln(x)}{x^{2}}dx
limit as x approaches 4 of x+3	\lim\:_{x\to\:4}(x+3)
derivative of sqrt(x)dx	\frac{d}{dx}(\sqrt{x}dx)
derivative of (1+x^{-3})	\frac{d}{dx}((1+x)^{-3})
area sqrt(2x), x/2 ,0,8	area\:\sqrt{2x},\frac{x}{2},0,8
taylor ln(1)+x	taylor\:\ln(1)+x
integral of (t+1/t)^{3/2}((t^2-1)/(t^2))	\int\:(t+\frac{1}{t})^{\frac{3}{2}}(\frac{t^{2}-1}{t^{2}})dt
integral of (cos(x))/(3-sin(x))	\int\:\frac{\cos(x)}{3-\sin(x)}dx
integral of 1/(sqrt(e^{2y)-1)}	\int\:\frac{1}{\sqrt{e^{2y}-1}}dy
integral from 0 to pi/4 of x^2sin(2x)	\int\:_{0}^{\frac{π}{4}}x^{2}\sin(2x)dx
derivative of cos(x+ln(cos(x))+xsin(x))	\frac{d}{dx}(\cos(x)+\ln(\cos(x))+x\sin(x))
integral of (x^3)/(1+x^3)	\int\:\frac{x^{3}}{1+x^{3}}dx
limit as x approaches 1 of x^2+2x-2	\lim\:_{x\to\:1}(x^{2}+2x-2)
tangent of f(x)=4e^x-x^{16}x,\at x=0	tangent\:f(x)=4e^{x}-x^{16}x,\at\:x=0
(\partial)/(\partial x)(pi*(x/2)^2h)	\frac{\partial\:}{\partial\:x}(π\cdot\:(\frac{x}{2})^{2}h)
derivative of 1/(4x^2+3x)	derivative\:\frac{1}{4x^{2}+3x}
integral of 36e^{4x}sqrt(3+e^{4x)}	\int\:36e^{4x}\sqrt{3+e^{4x}}dx
d/(dy)(arctan(y))	\frac{d}{dy}(\arctan(y))
sin(x)y^'=y+2x	\sin(x)y^{\prime\:}=y+2x
integral of (cos(x)+1/9 x)	\int\:(\cos(x)+\frac{1}{9}x)dx
limit as x approaches 1 of (2-7x)/(x+6)	\lim\:_{x\to\:1}(\frac{2-7x}{x+6})
derivative of 5log_{10}(x)	derivative\:5\log_{10}(x)
y^{''}-7y^'=49t,y(0)=7,y^'(0)=0	y^{\prime\:\prime\:}-7y^{\prime\:}=49t,y(0)=7,y^{\prime\:}(0)=0
limit as x approaches 0 of 1/(x^2)	\lim\:_{x\to\:0}(\frac{1}{x^{2}})
y^{''}+4y^'+5y=35e^{-4x},y(0)=-2,y^'(0)=1	y^{\prime\:\prime\:}+4y^{\prime\:}+5y=35e^{-4x},y(0)=-2,y^{\prime\:}(0)=1
limit as x approaches 0 of (1+x^2)-1	\lim\:_{x\to\:0}((1+x^{2})-1)
derivative of cos^2(xsin(x))	\frac{d}{dx}(\cos^{2}(x)\sin(x))
derivative of (x^3+5)ex	derivative\:(x^{3}+5)ex
integral of (x^4)/(x+4)	\int\:\frac{x^{4}}{x+4}dx
(\partial)/(\partial z)((e^{xz+y})/(z^2+w))	\frac{\partial\:}{\partial\:z}(\frac{e^{xz+y}}{z^{2}+w})
derivative of sin(t)	derivative\:\sin(t)
integral of ln(x^3)	\int\:\ln(x^{3})dx
derivative of 7e^x(sqrt(x))	\frac{d}{dx}(7e^{x}(\sqrt{x}))
derivative of (x^4)/(4-x^3)	derivative\:\frac{x^{4}}{4-x^{3}}
(\partial)/(\partial s)(t-2s)	\frac{\partial\:}{\partial\:s}(t-2s)
integral of (x+5)/((x+4)(x^2-1))	\int\:\frac{x+5}{(x+4)(x^{2}-1)}dx
integral of sqrt(25-x^2)(2x)	\int\:\sqrt{25-x^{2}}(2x)dx
(\partial)/(\partial x)((-t^2)/((1-x^2)))	\frac{\partial\:}{\partial\:x}(\frac{-t^{2}}{(1-x^{2})})
y^'-2y=x+5	y^{\prime\:}-2y=x+5
limit as x approaches (5pi)/2-of sec(x)	\lim\:_{x\to\:\frac{5π}{2}-}(\sec(x))
integral of y/(z^2)	\int\:\frac{y}{z^{2}}dz
derivative of sqrt(\sqrt{x)-1}	\frac{d}{dx}(\sqrt{\sqrt{x}-1})
integral from 2 to 5 of e^{4x}	\int\:_{2}^{5}e^{4x}dx
derivative of 5^{-x^2}	\frac{d}{dx}(5^{-x^{2}})
integral from 0 to 2pi of sin^2(5x)	\int\:_{0}^{2π}\sin^{2}(5x)dx
integral of t/(sqrt(9+t^2))	\int\:\frac{t}{\sqrt{9+t^{2}}}dt
(\partial)/(\partial m)(mx+b)	\frac{\partial\:}{\partial\:m}(mx+b)
integral of (1-1/x)^2	\int\:(1-\frac{1}{x})^{2}dx
sum from n=1 to infinity of (3^n)/(4^n)	\sum\:_{n=1}^{\infty\:}\frac{3^{n}}{4^{n}}
integral from 9 to 16 of sqrt(x)	\int\:_{9}^{16}\sqrt{x}dx
derivative of sin((pix/8))	\frac{d}{dx}(\sin(\frac{πx}{8}))
sum from n=0 to infinity of 1/(n(ln(n)))	\sum\:_{n=0}^{\infty\:}\frac{1}{n(\ln(n))}
derivative of f(x)=sin(x)+2/3 cot(x)	derivative\:f(x)=\sin(x)+\frac{2}{3}\cot(x)
integral of x/((x+2))	\int\:\frac{x}{(x+2)}dx
y^{''}+121y^'=cos(10t)	y^{\prime\:\prime\:}+121y^{\prime\:}=\cos(10t)
derivative of f(x)=5x^{3/2}	derivative\:f(x)=5x^{\frac{3}{2}}
integral of 4x^3-2x^2	\int\:4x^{3}-2x^{2}dx
integral of 6x*e^{x^2-2}	\int\:6x\cdot\:e^{x^{2}-2}dx
d/(dz)(sin(z))	\frac{d}{dz}(\sin(z))
integral of 1/(sqrt(-u^2+b-a))	\int\:\frac{1}{\sqrt{-u^{2}+b-a}}du
limit as x approaches infinity of (x-xsqrt(x))/(2x^{3/2)+3x-5}	\lim\:_{x\to\:\infty\:}(\frac{x-x\sqrt{x}}{2x^{\frac{3}{2}}+3x-5})
derivative of 9sqrt(x+10)	derivative\:9\sqrt{x+10}
limit as x approaches 0+of (x)^{4x}	\lim\:_{x\to\:0+}((x)^{4x})
integral of (x/(sqrt(x-1)))	\int\:(\frac{x}{\sqrt{x-1}})dx
limit as x approaches θ of x^2-5	\lim\:_{x\to\:θ}(x^{2}-5)
integral of x/(sqrt(3+x^2))	\int\:\frac{x}{\sqrt{3+x^{2}}}dx
limit as x approaches 2 of (4-x^2)/(2-x)	\lim\:_{x\to\:2}(\frac{4-x^{2}}{2-x})
limit as x approaches 0 of tan(x)-sin(x)	\lim\:_{x\to\:0}(\tan(x)-\sin(x))
limit as x approaches a of 1/(0-10)	\lim\:_{x\to\:a}(\frac{1}{0-10})
derivative of 1/((x-2))	derivative\:\frac{1}{(x-2)}
derivative of sqrt(5θ)	derivative\:\sqrt{5θ}
derivative of f(x)=-2x-1	derivative\:f(x)=-2x-1
derivative of 4x^2sqrt(25-x^2)	derivative\:4x^{2}\sqrt{25-x^{2}}
sum from n=1 to infinity of 6/((3n+1)^2)	\sum\:_{n=1}^{\infty\:}\frac{6}{(3n+1)^{2}}
y^{''}=e^x	y^{\prime\:\prime\:}=e^{x}
integral from 0 to 16 of xsqrt(x)	\int\:_{0}^{16}x\sqrt{x}dx
derivative of f(x)=ln(x^2-4x+1)	derivative\:f(x)=\ln(x^{2}-4x+1)
y^'+5xy=6x	y^{\prime\:}+5xy=6x
slope of y=6+5x^2+2x^3	slope\:y=6+5x^{2}+2x^{3}
integral of (2x)/(sqrt(x^4+16))	\int\:\frac{2x}{\sqrt{x^{4}+16}}dx
area 3cos(2x),3-3cos(2x)	area\:3\cos(2x),3-3\cos(2x)
x^2*y^'+(2-y)=0	x^{2}\cdot\:y^{\prime\:}+(2-y)=0
(\partial)/(\partial x)((2x+3y)^{10})	\frac{\partial\:}{\partial\:x}((2x+3y)^{10})
derivative of e^x*sin(x)	\frac{d}{dx}(e^{x}\cdot\:\sin(x))
limit as x approaches 0 of 2x^2-x	\lim\:_{x\to\:0}(2x^{2}-x)
integral of cos^{11}(x)sin(x)	\int\:\cos^{11}(x)\sin(x)dx
inverse oflaplace 2(1/(s-3))	inverselaplace\:2(\frac{1}{s-3})
integral of e^{2y}cos(3y)	\int\:e^{2y}\cos(3y)dy
(\partial)/(\partial x)(3xcos(x)cos(y))	\frac{\partial\:}{\partial\:x}(3x\cos(x)\cos(y))
derivative of sqrt(x)-6	derivative\:\sqrt{x}-6
integral of (x^4)/(5-x^5)	\int\:\frac{x^{4}}{5-x^{5}}dx
(\partial)/(\partial x)(yln(y^2-2x))	\frac{\partial\:}{\partial\:x}(y\ln(y^{2}-2x))
integral of (x^2*ln(x))	\int\:(x^{2}\cdot\:\ln(x))dx
derivative of 1/(t^4)	derivative\:\frac{1}{t^{4}}
integral of (sin(y)-ysin(x))	\int\:(\sin(y)-y\sin(x))dx
(\partial)/(\partial t)(x+ysin(t))	\frac{\partial\:}{\partial\:t}(x+y\sin(t))

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