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Popular Calculus Problems

tangent of f(x)=4-x^2,\at x=-1	tangent\:f(x)=4-x^{2},\at\:x=-1
integral of 1/(10x^7)	\int\:\frac{1}{10x^{7}}dx
y'=y(3-y)	y\prime\:=y(3-y)
integral of (cos(y)sin(x))	\int\:(\cos(y)\sin(x))dy
integral of (9sec^2(x))/(tan(x))	\int\:\frac{9\sec^{2}(x)}{\tan(x)}dx
limit as x approaches 2 of sqrt(x)+x	\lim\:_{x\to\:2}(\sqrt{x}+x)
integral of (pix^4)/(16)	\int\:\frac{πx^{4}}{16}dx
y^'+1/x y=-1/x y^2,y(1)=2	y^{\prime\:}+\frac{1}{x}y=-\frac{1}{x}y^{2},y(1)=2
derivative of log_{5}(4/(x^2sqrt(1-x)))	\frac{d}{dx}(\log_{5}(\frac{4}{x^{2}\sqrt{1-x}}))
integral of-4x^2e^{-3x}	\int\:-4x^{2}e^{-3x}dx
limit as x approaches 1 of (f(x))x^2-2x	\lim\:_{x\to\:1}((f(x))x^{2}-2x)
limit as h approaches 0 of h^2+5^h	\lim\:_{h\to\:0}(h^{2}+5^{h})
integral of e^{-7x}	\int\:e^{-7x}dx
limit as x approaches infinity of 1+3/x	\lim\:_{x\to\:\infty\:}(1+\frac{3}{x})
area 6x^2,x^2+2	area\:6x^{2},x^{2}+2
sum from n=2 to infinity of (1/3)^n	\sum\:_{n=2}^{\infty\:}(\frac{1}{3})^{n}
derivative of 5x^4-2x^3-3x+2	\frac{d}{dx}(5x^{4}-2x^{3}-3x+2)
y^{''}+8y^'+7y=0	y^{\prime\:\prime\:}+8y^{\prime\:}+7y=0
integral of sin(x)cos(x)sqrt(1-sin^4(x))	\int\:\sin(x)\cos(x)\sqrt{1-\sin^{4}(x)}dx
(\partial)/(\partial x)((3y)*(2x)^{-1})	\frac{\partial\:}{\partial\:x}((3y)\cdot\:(2x)^{-1})
parity f(x)=sin(tan(2x))	parity\:f(x)=\sin(\tan(2x))
derivative of 2(2x^5-3x+2)^8	derivative\:2(2x^{5}-3x+2)^{8}
integral of 3xy	\int\:3xy
integral of 1/((2-x)sqrt(1-x))	\int\:\frac{1}{(2-x)\sqrt{1-x}}dx
integral of (t+7)e^{2t+3}	\int\:(t+7)e^{2t+3}dt
derivative of sqrt(5)x+sqrt(6x)	\frac{d}{dx}(\sqrt{5}x+\sqrt{6x})
area y^2-7x=1,x-y=1	area\:y^{2}-7x=1,x-y=1
integral of 6e^5	\int\:6e^{5}dx
derivative of (x-1(x^2+x+1))	\frac{d}{dx}((x-1)(x^{2}+x+1))
derivative of-2ln(-x)	\frac{d}{dx}(-2\ln(-x))
taylor (sin(x))/x	taylor\:\frac{\sin(x)}{x}
limit as x approaches-6-of x^2+6	\lim\:_{x\to\:-6-}(x^{2}+6)
derivative of sqrt(7)x+sqrt(2x)	\frac{d}{dx}(\sqrt{7}x+\sqrt{2x})
derivative of 1+cos(6x)	\frac{d}{dx}(1+\cos(6x))
(x^2-1)y^'=xyln(y)	(x^{2}-1)y^{\prime\:}=xy\ln(y)
integral from 1 to infinity of x^{-4/3}	\int\:_{1}^{\infty\:}x^{-\frac{4}{3}}dx
(\partial)/(\partial x)(e^{-x^2-2y^2})	\frac{\partial\:}{\partial\:x}(e^{-x^{2}-2y^{2}})
integral of 8sec(x)(sec(x)-4tan(x))	\int\:8\sec(x)(\sec(x)-4\tan(x))dx
y^{''}+8y^'+4y=t	y^{\prime\:\prime\:}+8y^{\prime\:}+4y=t
(\partial)/(\partial y)(sin(z))	\frac{\partial\:}{\partial\:y}(\sin(z))
area 4sqrt(x+9),sqrt(144-x),-9,144	area\:4\sqrt{x+9},\sqrt{144-x},-9,144
derivative of 2/(x^3)-8/x	derivative\:\frac{2}{x^{3}}-\frac{8}{x}
derivative of y=((f(x))/(g(x)))^2	derivative\:y=(\frac{f(x)}{g(x)})^{2}
integral of x^4e^{2x}	\int\:x^{4}e^{2x}dx
integral of (2x+1)/((3x-1)(x^2+2x+2))	\int\:\frac{2x+1}{(3x-1)(x^{2}+2x+2)}dx
(\partial)/(\partial x)(4-2*(3x-y)^2)	\frac{\partial\:}{\partial\:x}(4-2\cdot\:(3x-y)^{2})
slope of y=-(-6x+6)^{1/2},x=-5	slope\:y=-(-6x+6)^{\frac{1}{2}},x=-5
d/(dv)(ae^v+b/v+c/(v^2))	\frac{d}{dv}(ae^{v}+\frac{b}{v}+\frac{c}{v^{2}})
xy^'-2y+y^2=0	xy^{\prime\:}-2y+y^{2}=0
y^{''}+2ky^'+k^4y=0	y^{\prime\:\prime\:}+2ky^{\prime\:}+k^{4}y=0
slope of (9,12),(-2,-17)	slope\:(9,12),(-2,-17)
integral of (x^2)/((x+1)(x+2)^2)	\int\:\frac{x^{2}}{(x+1)(x+2)^{2}}dx
integral of x^2e^{xy}	\int\:x^{2}e^{xy}dy
integral of e^{(-x)/3}	\int\:e^{\frac{-x}{3}}dx
integral from-2 to 3 of (27)/(x^4)	\int\:_{-2}^{3}\frac{27}{x^{4}}dx
xy^2y^'=y^3-1x^3	xy^{2}y^{\prime\:}=y^{3}-1x^{3}
(\partial)/(\partial y)((-x)/((x+y)^2))	\frac{\partial\:}{\partial\:y}(\frac{-x}{(x+y)^{2}})
integral from 0 to 1 of xsqrt(8-x^2)	\int\:_{0}^{1}x\sqrt{8-x^{2}}dx
(1+ln(x)+y/x)dx=(7-ln(x))dy	(1+\ln(x)+\frac{y}{x})dx=(7-\ln(x))dy
limit as x approaches-7 of sqrt(1/(x+7))	\lim\:_{x\to\:-7}(\sqrt{\frac{1}{x+7}})
laplacetransform [t]	laplacetransform\:[t]
derivative of ln(e^{6x})	\frac{d}{dx}(\ln(e^{6x}))
integral of (1/(sqrt(9-x^2)))	\int\:(\frac{1}{\sqrt{9-x^{2}}})dx
f^{''}(x)=(7+6x)^{e^{-5x}}	f^{\prime\:\prime\:}(x)=(7+6x)^{e^{-5x}}
integral of sqrt(x)(3-5x)	\int\:\sqrt{x}(3-5x)dx
derivative of cos^3(e^{-x})	\frac{d}{dx}(\cos^{3}(e^{-x}))
integral of cos((mpix)/3)	\int\:\cos(\frac{mπx}{3})dx
(\partial)/(\partial y)(2ycos(x))	\frac{\partial\:}{\partial\:y}(2y\cos(x))
y^{''}+2y^'+2y=sin(sqrt(2)x)	y^{\prime\:\prime\:}+2y^{\prime\:}+2y=\sin(\sqrt{2}x)
limit as x approaches 0+of e^{-5/x}	\lim\:_{x\to\:0+}(e^{-\frac{5}{x}})
integral of 1/(sqrt(-x^2+14x+50))	\int\:\frac{1}{\sqrt{-x^{2}+14x+50}}dx
derivative of sqrt(1+sin^2(e^{5x))}	derivative\:\sqrt{1+\sin^{2}(e^{5x})}
derivative of ln(x+sqrt(x^2+3))	\frac{d}{dx}(\ln(x+\sqrt{x^{2}+3}))
2x(1+y)dx-ydy=0	2x(1+y)dx-ydy=0
derivative of x^8ln(x)	derivative\:x^{8}\ln(x)
f(x)=e^{3sqrt(x)}	f(x)=e^{3\sqrt{x}}
f(x)=3^{xln(x)}	f(x)=3^{x\ln(x)}
laplacetransform e^{4t}sin(2t)	laplacetransform\:e^{4t}\sin(2t)
d/(dy)(y/(t^2+y^2))	\frac{d}{dy}(\frac{y}{t^{2}+y^{2}})
(dr)/(dt)+2tr-r=0,r(0)=6	\frac{dr}{dt}+2tr-r=0,r(0)=6
(\partial)/(\partial y)(sin(3x-4y))	\frac{\partial\:}{\partial\:y}(\sin(3x-4y))
integral of 1/(x^2+5)	\int\:\frac{1}{x^{2}+5}dx
limit as x approaches 2 of (-2)/(x(x-2))	\lim\:_{x\to\:2}(\frac{-2}{x(x-2)})
derivative of f(x)=(e^x)/(4x+1)	derivative\:f(x)=\frac{e^{x}}{4x+1}
integral of (3x^2+2)/((x^3+2x)^2)	\int\:\frac{3x^{2}+2}{(x^{3}+2x)^{2}}dx
tangent of y=(2x)/(x+1),(1,1)	tangent\:y=\frac{2x}{x+1},(1,1)
derivative of (5x/(x+1))	\frac{d}{dx}(\frac{5x}{x+1})
limit as x approaches+(-1) of (sin(x))/x	\lim\:_{x\to\:+(-1)}(\frac{\sin(x)}{x})
(dy)/(dx)=y^3	\frac{dy}{dx}=y^{3}
tangent of f(x)= x/(9-sqrt(x))	tangent\:f(x)=\frac{x}{9-\sqrt{x}}
sum from n=1 to infinity of (-1/3)^{n-1}	\sum\:_{n=1}^{\infty\:}(-\frac{1}{3})^{n-1}
tangent of x^3sqrt(x^3+3)	tangent\:x^{3}\sqrt{x^{3}+3}
integral from 1 to infinity of x/(4+x^2)	\int\:_{1}^{\infty\:}\frac{x}{4+x^{2}}dx
(\partial)/(\partial x)(ln(y-2x))	\frac{\partial\:}{\partial\:x}(\ln(y-2x))
(x+y)^2dx+(2xy+x^2-1)dy=0	(x+y)^{2}dx+(2xy+x^{2}-1)dy=0
derivative of f(x)=2^{50}	derivative\:f(x)=2^{50}
integral of x(1-x)^7	\int\:x(1-x)^{7}dx
tangent of f(x)=3x^3+3x^2-11x-1	tangent\:f(x)=3x^{3}+3x^{2}-11x-1
y^{''}+9y=3csc^2(3t)	y^{\prime\:\prime\:}+9y=3\csc^{2}(3t)
integral of sinh(2x)	\int\:\sinh(2x)dx

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