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Popular Calculus Problems

integral from 0 to 2 of 1/(sqrt(2-x))	\int\:_{0}^{2}\frac{1}{\sqrt{2-x}}dx
integral of (sin(x))^{-1}	\int\:(\sin(x))^{-1}dx
area-x,x-x^2,0,2	area\:-x,x-x^{2},0,2
integral of (x^3)/1+x^4	\int\:\frac{x^{3}}{1}+x^{4}dx
integral of cos(n*x)	\int\:\cos(n\cdot\:x)dx
sum from n=1 to infinity of 1/((2n+1)^3)	\sum\:_{n=1}^{\infty\:}\frac{1}{(2n+1)^{3}}
derivative of log_{4}(\sqrt[3]{x})	\frac{d}{dx}(\log_{4}(\sqrt[3]{x}))
integral of 1/(x^4+4x^2+4)	\int\:\frac{1}{x^{4}+4x^{2}+4}dx
derivative of ln(w(h-l)+pi-T)+ln(l)	derivative\:\ln(w(h-l)+π-T)+\ln(l)
(\partial)/(\partial x)(x^2+3xy)	\frac{\partial\:}{\partial\:x}(x^{2}+3xy)
derivative of y= x/6-6/x	derivative\:y=\frac{x}{6}-\frac{6}{x}
(\partial)/(\partial x)(-0.1cos(6x))	\frac{\partial\:}{\partial\:x}(-0.1\cdot\:\cos(6\cdot\:x))
limit as x approaches 0 of (-11x^2+9x)/x	\lim\:_{x\to\:0}(\frac{-11x^{2}+9x}{x})
integral of xsin(3+3x)	\int\:x\sin(3+3x)dx
integral of (1/5 x^5+1/3 x^4-x)	\int\:(\frac{1}{5}x^{5}+\frac{1}{3}x^{4}-x)dx
limit as x approaches 0 of (1-2x)^{(1/x)}	\lim\:_{x\to\:0}((1-2x)^{(\frac{1}{x})})
derivative of ln(10x^2-8)	\frac{d}{dx}(\ln(10x^{2}-8))
y^'=e^{2t+y-1}-2	y^{\prime\:}=e^{2t+y-1}-2
(\partial)/(\partial x)(e^{xy}+ln(x/y))	\frac{\partial\:}{\partial\:x}(e^{xy}+\ln(\frac{x}{y}))
(\partial)/(\partial x)(2xy^2+4)	\frac{\partial\:}{\partial\:x}(2xy^{2}+4)
limit as w approaches infinity of (2w^2-3w+4)/(5w^2+7w-1)	\lim\:_{w\to\:\infty\:}(\frac{2w^{2}-3w+4}{5w^{2}+7w-1})
y^{''}-ky=0	y^{\prime\:\prime\:}-ky=0
limit as x approaches-2 of (x-6)^{2/3}	\lim\:_{x\to\:-2}((x-6)^{\frac{2}{3}})
y^'=0.2ln((2000)/y)y	y^{\prime\:}=0.2\ln(\frac{2000}{y})y
derivative of 6/(1+cos(x))	\frac{d}{dx}(\frac{6}{1+\cos(x)})
limit as x approaches infinity of 0	\lim\:_{x\to\:\infty\:}(0)
y^{''}+8y^'+16y=5e^{-4t}	y^{\prime\:\prime\:}+8y^{\prime\:}+16y=5e^{-4t}
integral of e^{-19x}	\int\:e^{-19x}dx
area-3x-x^2,-10	area\:-3x-x^{2},-10
y^'=9x+y,y(0)=3	y^{\prime\:}=9x+y,y(0)=3
derivative of y=x^2sqrt(9-x^2)	derivative\:y=x^{2}\sqrt{9-x^{2}}
limit as x approaches 0 of (7x)/(sin(x))	\lim\:_{x\to\:0}(\frac{7x}{\sin(x)})
derivative of f(x)=sqrt(5x+6)	derivative\:f(x)=\sqrt{5x+6}
integral of sqrt(cos(2x))	\int\:\sqrt{\cos(2x)}dx
(dP)/(dt)=-1/2 P+t	\frac{dP}{dt}=-\frac{1}{2}P+t
(dy)/(dx)=x^2sec(y)	\frac{dy}{dx}=x^{2}\sec(y)
derivative of 3x*e^{2x}	\frac{d}{dx}(3x\cdot\:e^{2x})
limit as x approaches infinity of (e^{1/x})/(arctan(x))	\lim\:_{x\to\:\infty\:}(\frac{e^{\frac{1}{x}}}{\arctan(x)})
integral of 7xsin(x)	\int\:7x\sin(x)dx
inverse oflaplace (10)/(s^2)	inverselaplace\:\frac{10}{s^{2}}
(\partial)/(\partial x)(10^{x^2-1})	\frac{\partial\:}{\partial\:x}(10^{x^{2}-1})
integral of 1/(2xln(x))	\int\:\frac{1}{2x\ln(x)}dx
derivative of y=\sqrt[5]{x^3}-x^pi	derivative\:y=\sqrt[5]{x^{3}}-x^{π}
derivative of (7x/(x^2+49))	\frac{d}{dx}(\frac{7x}{x^{2}+49})
(d^4)/(dx^4)(4e^{x^2})	\frac{d^{4}}{dx^{4}}(4e^{x^{2}})
integral of 3/(x^2(x-1))	\int\:\frac{3}{x^{2}(x-1)}dx
(\partial)/(\partial x)(y^2ln(x))	\frac{\partial\:}{\partial\:x}(y^{2}\ln(x))
integral of (x^6-5x)/(x^4)	\int\:\frac{x^{6}-5x}{x^{4}}dx
derivative of e^2(sin(pi/4-1))	\frac{d}{dx}(e^{2}(\sin(\frac{π}{4})-1))
inverse oflaplace (s-1)/(2s^2+8s+11)	inverselaplace\:\frac{s-1}{2s^{2}+8s+11}
derivative of sqrt(1+5x)	derivative\:\sqrt{1+5x}
integral of (x+4)/(x^3+3x^2+2x)	\int\:\frac{x+4}{x^{3}+3x^{2}+2x}dx
derivative of (a^{2/3}-x^{2/3}^{3/2})	\frac{d}{dx}((a^{\frac{2}{3}}-x^{\frac{2}{3}})^{\frac{3}{2}})
derivative of (arcsin(x)/(arctan(x)))	\frac{d}{dx}(\frac{\arcsin(x)}{\arctan(x)})
derivative of f(x)=x^3-4x	derivative\:f(x)=x^{3}-4x
integral of (tan(x)sec^2(y))	\int\:(\tan(x)\sec^{2}(y))dx
derivative of (a+bx^3)	\frac{d}{dx}((a+bx)^{3})
limit as x approaches 2 of x^2-4x+1	\lim\:_{x\to\:2}(x^{2}-4x+1)
integral of 1/((1+x^4))	\int\:\frac{1}{(1+x^{4})}dx
integral of (x^4)/((7+x^5)^2)	\int\:\frac{x^{4}}{(7+x^{5})^{2}}dx
sum from n=2 to infinity of (3^n)/(12^n)	\sum\:_{n=2}^{\infty\:}\frac{3^{n}}{12^{n}}
4y^{''}-4y^'+y=8e^{x/2}	4y^{\prime\:\prime\:}-4y^{\prime\:}+y=8e^{\frac{x}{2}}
derivative of y=8e^{17t}	derivative\:y=8e^{17t}
derivative of 4csc(5x)	derivative\:4\csc(5x)
f(t)=4t^2	f(t)=4t^{2}
(\partial)/(\partial x)(Ae^{i(kx-wt)})	\frac{\partial\:}{\partial\:x}(Ae^{i(kx-wt)})
(\partial)/(\partial x)(ln(sin^2(x)))	\frac{\partial\:}{\partial\:x}(\ln(\sin^{2}(x)))
sum from n=0 to infinity of 2^n*(1/4)^{ln(2^n)}	\sum\:_{n=0}^{\infty\:}2^{n}\cdot\:(\frac{1}{4})^{\ln(2^{n})}
(d^2y)/(dx^2)=4e^{-x},y(0)=3,y^'(0)=2	\frac{d^{2}y}{dx^{2}}=4e^{-x},y(0)=3,y^{\prime\:}(0)=2
derivative of 1/(2sqrt(r))+1/(3r^{2/3)}	derivative\:\frac{1}{2\sqrt{r}}+\frac{1}{3r^{\frac{2}{3}}}
limit as y approaches infinity of 1/5 (2y^2+3y)x	\lim\:_{y\to\:\infty\:}(\frac{1}{5}(2y^{2}+3y)x)
area 2-x^2,10-6x	area\:2-x^{2},10-6x
integral from 0 to 0.4 of 300x	\int\:_{0}^{0.4}300xdx
integral of (\sqrt[3]{x})^4	\int\:(\sqrt[3]{x})^{4}dx
derivative of x^2log_{2}(x^3)	\frac{d}{dx}(x^{2}\log_{2}(x^{3}))
laplacetransform u^5	laplacetransform\:u^{5}
derivative of (x^4/3-7x)	\frac{d}{dx}(\frac{x^{4}}{3}-7x)
derivative of e^{-2t}	derivative\:e^{-2t}
derivative of xsqrt(5)	\frac{d}{dx}(x\sqrt{5})
sum from n=1 to infinity of ((-1))/n	\sum\:_{n=1}^{\infty\:}\frac{(-1)}{n}
inverse oflaplace s/((s^2+3^2)^2)	inverselaplace\:\frac{s}{(s^{2}+3^{2})^{2}}
sum from n=2 to infinity of 1/(4^n)	\sum\:_{n=2}^{\infty\:}\frac{1}{4^{n}}
integral from 0 to 1 of tsqrt(9t^2+4)	\int\:_{0}^{1}t\sqrt{9t^{2}+4}dt
inverse oflaplace x/(x+8)	inverselaplace\:\frac{x}{x+8}
integral of (cos(x))/x	\int\:\frac{\cos(x)}{x}dx
tangent of 5x^2-7x	tangent\:5x^{2}-7x
derivative of axe^{bx}	\frac{d}{dx}(a\cdot\:x\cdot\:e^{bx})
integral of (y-1)/(-y-1)	\int\:\frac{y-1}{-y-1}dy
(\partial)/(\partial y)(2(y+1)e^{2x})	\frac{\partial\:}{\partial\:y}(2(y+1)e^{2x})
slope ofintercept (-6,3),(4,-1)	slopeintercept\:(-6,3),(4,-1)
derivative of-19.6x+2	derivative\:-19.6x+2
integral of x\sqrt[4]{x+20}	\int\:x\sqrt[4]{x+20}dx
integral of 1/(sqrt(\sqrt{x)+1)}	\int\:\frac{1}{\sqrt{\sqrt{x}+1}}dx
(\partial)/(\partial y)(x^2-4xy+y^3+4y)	\frac{\partial\:}{\partial\:y}(x^{2}-4xy+y^{3}+4y)
integral of (2xyz+sin(x))	\int\:(2xyz+\sin(x))dx
derivative of x^4(x^2+1^6)	\frac{d}{dx}(x^{4}(x^{2}+1)^{6})
derivative of-5/((x+3^3))	\frac{d}{dx}(-\frac{5}{(x+3)^{3}})
taylor 1/((7+x)2)	taylor\:\frac{1}{(7+x)2}
limit as x approaches 0 of xsin(x)	\lim\:_{x\to\:0}(x\sin(x))
integral from 0 to ln(21) of xe^x	\int\:_{0}^{\ln(21)}xe^{x}dx

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