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Popular Calculus Problems

integral from 0 to 2 of e^{-3x}	\int\:_{0}^{2}e^{-3x}dx
y^{''}+y^'-6y=6t-7-(20te^{2t}+14e^{2t})	y^{\prime\:\prime\:}+y^{\prime\:}-6y=6t-7-(20te^{2t}+14e^{2t})
tangent of f(x)=x^6,\at x=2	tangent\:f(x)=x^{6},\at\:x=2
(dy)/(dx)=1+xy	\frac{dy}{dx}=1+xy
derivative of 2/x+1	\frac{d}{dx}(\frac{2}{x}+1)
x^'=5(1-x/(10))	x^{\prime\:}=5(1-\frac{x}{10})
y^{''}+4y^'+4y=xcos(2x)+3e^{-2x}	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=x\cos(2x)+3e^{-2x}
integral of tan^3(6x)sec^3(6x)	\int\:\tan^{3}(6x)\sec^{3}(6x)dx
limit as x approaches-2-of 1/(x^2+2x)	\lim\:_{x\to\:-2-}(\frac{1}{x^{2}+2x})
derivative of 1/(cosh(x))	\frac{d}{dx}(\frac{1}{\cosh(x)})
limit as x approaches 3 of (10)/(x-3)	\lim\:_{x\to\:3}(\frac{10}{x-3})
derivative of h=t^2(6t-4)^3	derivative\:h=t^{2}(6t-4)^{3}
(\partial)/(\partial x)(3ln(x)-5)	\frac{\partial\:}{\partial\:x}(3\ln(x)-5)
integral of (x-17)/(x^2+1)	\int\:\frac{x-17}{x^{2}+1}dx
(\partial)/(\partial x)(x^2sin(3xy))	\frac{\partial\:}{\partial\:x}(x^{2}\sin(3xy))
integral of sin(3x+1)	\int\:\sin(3x+1)dx
(\partial)/(\partial x)(5cos(2x+5y))	\frac{\partial\:}{\partial\:x}(5\cos(2x+5y))
integral of (5x^3)/(sqrt(6+x^2))	\int\:\frac{5x^{3}}{\sqrt{6+x^{2}}}dx
derivative of 2sin(2x)	\frac{d}{dx}(2\sin(2x))
(d^4)/(dx^4)(1/(x^2))	\frac{d^{4}}{dx^{4}}(\frac{1}{x^{2}})
integral of x^2cos(mpix)	\int\:x^{2}\cos(mπx)dx
tangent of sin(5x)+cos(4x)	tangent\:\sin(5x)+\cos(4x)
tangent of f(x)= 1/(x+2),\at x=0	tangent\:f(x)=\frac{1}{x+2},\at\:x=0
integral of 9x^3y+3y^2	\int\:9x^{3}y+3y^{2}dx
limit as x approaches 0-of 4(1/x-csc(x))	\lim\:_{x\to\:0-}(4(\frac{1}{x}-\csc(x)))
derivative of (1/3 (x^2+2)^{3/2})	\frac{d}{dx}((\frac{1}{3})(x^{2}+2)^{\frac{3}{2}})
(\partial)/(\partial x)(2y-x^2e^{-y})	\frac{\partial\:}{\partial\:x}(2y-x^{2}e^{-y})
laplacetransform t^3e^{b*t}	laplacetransform\:t^{3}e^{b\cdot\:t}
(\partial)/(\partial x)(ln(x+y^4))	\frac{\partial\:}{\partial\:x}(\ln(x+y^{4}))
limit as x approaches infinity of-x/2	\lim\:_{x\to\:\infty\:}(-\frac{x}{2})
limit as x approaches pi/2 of 5sin(x)	\lim\:_{x\to\:\frac{π}{2}}(5\sin(x))
tangent of f(x)=-9x^2,\at x=2	tangent\:f(x)=-9x^{2},\at\:x=2
maclaurin e^{(-x)/2}	maclaurin\:e^{\frac{-x}{2}}
slope of f(t)=2-4/t	slope\:f(t)=2-\frac{4}{t}
maclaurin e^{3x}	maclaurin\:e^{3x}
derivative of arccos(arcsin(x))	\frac{d}{dx}(\arccos(\arcsin(x)))
(\partial)/(\partial x)(3xln(y)+yln(z)-4x)	\frac{\partial\:}{\partial\:x}(3x\ln(y)+y\ln(z)-4x)
derivative of y=3sin(x^3-5x^2+8x+0.5)	derivative\:y=3\sin(x^{3}-5x^{2}+8x+0.5)
integral of 2x(x^2+1)^{-4}	\int\:2x(x^{2}+1)^{-4}dx
inverse oflaplace 7/(s^3+2s^2+9s+18)	inverselaplace\:\frac{7}{s^{3}+2s^{2}+9s+18}
integral of (e^x)/(e^{-6x)}	\int\:\frac{e^{x}}{e^{-6x}}dx
derivative of (5x/(9x^2+1))	\frac{d}{dx}(\frac{5x}{9x^{2}+1})
y^'=y-k	y^{\prime\:}=y-k
(x^2-4)((dy)/(dx))+4y=(x+2)^2	(x^{2}-4)(\frac{dy}{dx})+4y=(x+2)^{2}
slope of (-7,-7),(-3,6)	slope\:(-7,-7),(-3,6)
integral of (cos^4(x))/(sin^6(x))	\int\:\frac{\cos^{4}(x)}{\sin^{6}(x)}dx
integral of-7csc^2(x)	\int\:-7\csc^{2}(x)dx
y^{''}+y=k(e^{(-at)}-e^{(-b*t)})	y^{\prime\:\prime\:}+y=k\cdot\:(e^{(-a\cdot\:t)}-e^{(-b\cdot\:t)})
integral of x^{-3}ln(x)	\int\:x^{-3}\ln(x)dx
(\partial)/(\partial s)(e^{s+t})	\frac{\partial\:}{\partial\:s}(e^{s+t})
(\partial)/(\partial x)(5(y-3)^3(x-6))	\frac{\partial\:}{\partial\:x}(5\cdot\:(y-3)^{3}\cdot\:(x-6))
(\partial)/(\partial y)(x^{8y})	\frac{\partial\:}{\partial\:y}(x^{8y})
(\partial)/(\partial s)(t^2)	\frac{\partial\:}{\partial\:s}(t^{2})
(\partial)/(\partial x)(x^2-y)	\frac{\partial\:}{\partial\:x}(x^{2}-y)
(\partial)/(\partial x)(7-e^{xyz})	\frac{\partial\:}{\partial\:x}(7-e^{xyz})
integral of cos(θ)cos^5(sin(θ))	\int\:\cos(θ)\cos^{5}(\sin(θ))dθ
integral of x/(sqrt(ax+b))	\int\:\frac{x}{\sqrt{ax+b}}dx
derivative of (x-14/(sqrt(x)-\sqrt{14)})	\frac{d}{dx}(\frac{x-14}{\sqrt{x}-\sqrt{14}})
(\partial)/(\partial y)(e^{x/y})	\frac{\partial\:}{\partial\:y}(e^{\frac{x}{y}})
derivative of 10^{tan(2x})	\frac{d}{dx}(10^{\tan(2x)})
y^{''}+16y=sin(4x)	y^{\prime\:\prime\:}+16y=\sin(4x)
integral of (cosh(x))/(1+sinh(x))	\int\:\frac{\cosh(x)}{1+\sinh(x)}dx
integral of 1/((e^x+1))	\int\:\frac{1}{(e^{x}+1)}dx
derivative of (1+sin(x)/(cos(x)))	\frac{d}{dx}(\frac{1+\sin(x)}{\cos(x)})
y^'-(4y)/x =-2/(x^2)	y^{\prime\:}-\frac{4y}{x}=-\frac{2}{x^{2}}
tangent of (-6x)/(x^2+1)	tangent\:\frac{-6x}{x^{2}+1}
d/(dy)(2y^3)	\frac{d}{dy}(2y^{3})
integral of (sqrt(x^3-2))/x	\int\:\frac{\sqrt{x^{3}-2}}{x}dx
derivative of f(x)=(1-2t)/(1+6t)	derivative\:f(x)=\frac{1-2t}{1+6t}
derivative of f(x)=(5x)/(7x^2+1)	derivative\:f(x)=\frac{5x}{7x^{2}+1}
limit as x approaches-2.4 of [x]	\lim\:_{x\to\:-2.4}([x])
tangent of y= 4/(1+x^2),(1,2)	tangent\:y=\frac{4}{1+x^{2}},(1,2)
integral of (6-2x)/(9-x^2)	\int\:\frac{6-2x}{9-x^{2}}dx
integral of (5x-6)/(x^2+4)	\int\:\frac{5x-6}{x^{2}+4}dx
(\partial)/(\partial x)(sin(7x^4y-7xy^4))	\frac{\partial\:}{\partial\:x}(\sin(7x^{4}y-7xy^{4}))
y^{''}-10y^'+34y=0	y^{\prime\:\prime\:}-10y^{\prime\:}+34y=0
(\partial)/(\partial x)(x^{-1/2}cos(x))	\frac{\partial\:}{\partial\:x}(x^{-\frac{1}{2}}\cos(x))
inverse oflaplace (s-1)/(s(s^2+s+1))	inverselaplace\:\frac{s-1}{s(s^{2}+s+1)}
(\partial)/(\partial x)(e^{e^{xy}})	\frac{\partial\:}{\partial\:x}(e^{e^{xy}})
derivative of x\|x-2\|	derivative\:x\left\|x-2\right\|
limit as x approaches-2 of 2\|x+2\|	\lim\:_{x\to\:-2}(2\left\|x+2\right\|)
(\partial)/(\partial x)(ln(y+x))	\frac{\partial\:}{\partial\:x}(\ln(y+x))
integral from-2 to 4 of x	\int\:_{-2}^{4}xdx
integral of 1/(1-3u)	\int\:\frac{1}{1-3u}du
(\partial)/(\partial x)(4x^2+y^2-9y)	\frac{\partial\:}{\partial\:x}(4x^{2}+y^{2}-9y)
area 4sin(x),2cos(x),[0,0.8pi]	area\:4\sin(x),2\cos(x),[0,0.8π]
integral of x/(sqrt(x^2+81))	\int\:\frac{x}{\sqrt{x^{2}+81}}dx
integral from-pi to pi of x^2sin(nx)	\int\:_{-π}^{π}x^{2}\sin(nx)dx
integral of (ln(x^{28}))/x	\int\:\frac{\ln(x^{28})}{x}dx
integral of ((1-x))/(1+x^2)	\int\:\frac{(1-x)}{1+x^{2}}dx
(\partial)/(\partial x)(4x(x^2+y^2)-4a^2x)	\frac{\partial\:}{\partial\:x}(4x(x^{2}+y^{2})-4a^{2}x)
derivative of a/x	derivative\:\frac{a}{x}
inverse oflaplace s/((s-1))	inverselaplace\:\frac{s}{(s-1)}
y(1+x^2)y^'-x(6+y^2)=0	y(1+x^{2})y^{\prime\:}-x(6+y^{2})=0
derivative of y=5x^4e^x+e^xx^5	derivative\:y=5x^{4}e^{x}+e^{x}x^{5}
limit as x approaches 1 of-6+2x^2	\lim\:_{x\to\:1}(-6+2x^{2})
f(x)=(x+2)/(x^2)	f(x)=\frac{x+2}{x^{2}}
36y^{''}-y=0,y(-6)=1,y^'(-6)=-1	36y^{\prime\:\prime\:}-y=0,y(-6)=1,y^{\prime\:}(-6)=-1
limit as x approaches-5 of-6x	\lim\:_{x\to\:-5}(-6x)
(2xy-3x^2)dx+(x^2+y)dy=0	(2xy-3x^{2})dx+(x^{2}+y)dy=0

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