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Popular Calculus Problems

limit as x approaches 5.6 of 7.3x+8.4	\lim\:_{x\to\:5.6}(7.3x+8.4)
integral from 0 to 1/2 of arccos(x)	\int\:_{0}^{\frac{1}{2}}\arccos(x)dx
limit as (x,y) approaches (0,0) of y/x	\lim\:_{(x,y)\to\:(0,0)}(\frac{y}{x})
tangent of f(x)=(x^2-48)^4	tangent\:f(x)=(x^{2}-48)^{4}
derivative of 6x^{1/3}	\frac{d}{dx}(6x^{\frac{1}{3}})
integral of 11tan^3(θ)	\int\:11\tan^{3}(θ)dθ
integral of ((x^3))/(x^2+1)	\int\:\frac{(x^{3})}{x^{2}+1}dx
tangent of y=8sin(pix-y),(1,0)	tangent\:y=8\sin(πx-y),(1,0)
derivative of (3sin(x+sqrt(x))^3)	\frac{d}{dx}((3\sin(x)+\sqrt{x})^{3})
limit as x approaches 2 of (3-sqrt(4x+1))/((x^2-2x))	\lim\:_{x\to\:2}(\frac{3-\sqrt{4x+1}}{(x^{2}-2x)})
laplacetransform sin(t+(11pi)/2)	laplacetransform\:\sin(t+\frac{11π}{2})
limit as x approaches 1 of (3x)/(2x+2)	\lim\:_{x\to\:1}(\frac{3x}{2x+2})
y^'=(6x^5y)/(ln(y))	y^{\prime\:}=\frac{6x^{5}y}{\ln(y)}
y^{''}+6y^'-7y=0	y^{\prime\:\prime\:}+6y^{\prime\:}-7y=0
integral of 5e^xsec(e^x+2)	\int\:5e^{x}\sec(e^{x}+2)dx
integral from 6 to 8 of (68)/((x-6)^3)	\int\:_{6}^{8}\frac{68}{(x-6)^{3}}dx
integral of 3x^2+4x	\int\:3x^{2}+4xdx
f(x)=desqrt(x)	f(x)=de\sqrt{x}
integral from 0 to 1 of 4(x^2+1)e^{-x}	\int\:_{0}^{1}4(x^{2}+1)e^{-x}dx
limit as t approaches 0 of (e^t-t-1)/t	\lim\:_{t\to\:0}(\frac{e^{t}-t-1}{t})
integral from 0 to 2 of pi(e^{-x^2})^2	\int\:_{0}^{2}π(e^{-x^{2}})^{2}dx
derivative of f(x)=x^{-1/4}	derivative\:f(x)=x^{-\frac{1}{4}}
derivative of f(x)=e^{x/(x-1)}	derivative\:f(x)=e^{\frac{x}{x-1}}
tangent of e^x,\at x=ln(7)	tangent\:e^{x},\at\:x=\ln(7)
derivative of tan(e^{3t})+e^{tan(3t)}	derivative\:\tan(e^{3t})+e^{\tan(3t)}
derivative of f(x)=7e^xcos(x)	derivative\:f(x)=7e^{x}\cos(x)
limit as x approaches 2 of sqrt(7-x)	\lim\:_{x\to\:2}(\sqrt{7-x})
integral from 1 to infinity of x^{-1/3}	\int\:_{1}^{\infty\:}x^{-\frac{1}{3}}dx
d/(dt)(-e^{-4t}+4te^{-4t})	\frac{d}{dt}(-e^{-4t}+4te^{-4t})
taylor ((z+2))/(z^2)	taylor\:\frac{(z+2)}{z^{2}}
integral of x/(sqrt(x^2+6x+8))	\int\:\frac{x}{\sqrt{x^{2}+6x+8}}dx
derivative of (x^2+x-1/(x^2-1))	\frac{d}{dx}(\frac{x^{2}+x-1}{x^{2}-1})
integral of 6cot^4(x)	\int\:6\cot^{4}(x)dx
integral of 1/(t^3)cos(pi/(t^2))	\int\:\frac{1}{t^{3}}\cos(\frac{π}{t^{2}})dt
y^{''}-4y=e^{-2x}-2x,y(0)=0,y^'(0)=0	y^{\prime\:\prime\:}-4y=e^{-2x}-2x,y(0)=0,y^{\prime\:}(0)=0
y^{''}+y= 3/2 sin(x)	y^{\prime\:\prime\:}+y=\frac{3}{2}\sin(x)
simplify x/3 (2x+1)^3	simplify\:\frac{x}{3}(2x+1)^{3}
slope of (-2,5),(6,2)	slope\:(-2,5),(6,2)
integral of x+1sqrt(x)	\int\:x+1\sqrt{x}dx
integral of (1+x^3)^73x^2	\int\:(1+x^{3})^{7}3x^{2}dx
(\partial)/(\partial y)(x^2e^{xy})	\frac{\partial\:}{\partial\:y}(x^{2}e^{xy})
integral of (1-x)/(1+x)	\int\:\frac{1-x}{1+x}dx
(\partial)/(\partial x)((sin(x))/(r^2))	\frac{\partial\:}{\partial\:x}(\frac{\sin(x)}{r^{2}})
derivative of 9x^{ln(9x})	\frac{d}{dx}(9x^{\ln(9x)})
tangent of g(x)=-x^5+4x^2-2x+2	tangent\:g(x)=-x^{5}+4x^{2}-2x+2
integral of (sin(2x))/(18+cos^2(x))	\int\:\frac{\sin(2x)}{18+\cos^{2}(x)}dx
derivative of (4x^5-5x^4+6x-2/(x^4))	\frac{d}{dx}(\frac{4x^{5}-5x^{4}+6x-2}{x^{4}})
y^'+3y+5=0	y^{\prime\:}+3y+5=0
derivative of 3x^2+12x+6	\frac{d}{dx}(3x^{2}+12x+6)
area Y=(x^{1/2}),Y=6-x,Y=0	area\:Y=(x^{\frac{1}{2}}),Y=6-x,Y=0
integral of e^{x-3}	\int\:e^{x-3}dx
area e^x,e^{-3x},x=ln(4)	area\:e^{x},e^{-3x},x=\ln(4)
integral of (x^2-2)/(sqrt(x))	\int\:\frac{x^{2}-2}{\sqrt{x}}dx
derivative of (150000)/((4x+75)^2)	derivative\:\frac{150000}{(4x+75)^{2}}
derivative of pi^7+sqrt(3x)	derivative\:π^{7}+\sqrt{3x}
derivative of (x+1)^2(2-x)^2	derivative\:(x+1)^{2}(2-x)^{2}
(\partial)/(\partial x)(cos^7(x^4y^9))	\frac{\partial\:}{\partial\:x}(\cos^{7}(x^{4}y^{9}))
sum from n=1 to infinity of (1+1/n)^{-n}	\sum\:_{n=1}^{\infty\:}(1+\frac{1}{n})^{-n}
derivative of sin^4(2xcos^43x)	\frac{d}{dx}(\sin^{4}(2xco)s^{4}3x)
integral of sec^2(x)+3	\int\:\sec^{2}(x)+3dx
inverse oflaplace 7/(s(s^2+5s))	inverselaplace\:\frac{7}{s(s^{2}+5s)}
parity f(x)=x^{tan(x)}	parity\:f(x)=x^{\tan(x)}
integral from 0 to 0.6 of 125x	\int\:_{0}^{0.6}125xdx
integral of 4xsin(3x)	\int\:4x\sin(3x)dx
integral of e^{-y}cos(y)	\int\:e^{-y}\cos(y)dy
tangent of y=(x^2-3x+3),(2,1)	tangent\:y=(x^{2}-3x+3),(2,1)
integral of sqrt(45+4x-x^2)	\int\:\sqrt{45+4x-x^{2}}dx
derivative of y=(ln(x))^x	derivative\:y=(\ln(x))^{x}
integral of (6x^2-3x)/(x^2)	\int\:\frac{6x^{2}-3x}{x^{2}}dx
y^'=2t	y^{\prime\:}=2t
derivative of f(x)=x+11	derivative\:f(x)=x+11
integral of-4e^{2x}	\int\:-4e^{2x}dx
(dy)/(dx)=e^{(y-x)}	\frac{dy}{dx}=e^{(y-x)}
integral from 0 to infinity of xae^{-ax}	\int\:_{0}^{\infty\:}xae^{-ax}dx
y=0	y=0
integral of x*sin(2x)	\int\:x\cdot\:\sin(2x)dx
integral of 4\sqrt[3]{x}+3\sqrt[6]{x^5}	\int\:4\sqrt[3]{x}+3\sqrt[6]{x^{5}}dx
sqrt(1-x^2)y^'-sqrt(1-y^2)=0	\sqrt{1-x^{2}}y^{\prime\:}-\sqrt{1-y^{2}}=0
(\partial)/(\partial x)(7)	\frac{\partial\:}{\partial\:x}(7)
f(x)=ln(x^2+9)	f(x)=\ln(x^{2}+9)
derivative of 1/x+tan(x)	derivative\:\frac{1}{x}+\tan(x)
integral of 1/(-8sqrt(x)-8x)	\int\:\frac{1}{-8\sqrt{x}-8x}dx
tangent of f(x)=x^3-4x,\at x=-2	tangent\:f(x)=x^{3}-4x,\at\:x=-2
integral from 2 to 4 of (2x+5)/(5-x)	\int\:_{2}^{4}\frac{2x+5}{5-x}dx
y^'=xe^{-y}	y^{\prime\:}=xe^{-y}
3y^{''}+5y^'-2y=0	3y^{\prime\:\prime\:}+5y^{\prime\:}-2y=0
limit as x approaches 8-of ln(8-x)	\lim\:_{x\to\:8-}(\ln(8-x))
limit as x approaches 1 of ln(9x)+e^x	\lim\:_{x\to\:1}(\ln(9x)+e^{x})
integral of (3x-1)^3	\int\:(3x-1)^{3}dx
integral from 0 to infinity of xe^{-x}	\int\:_{0}^{\infty\:}xe^{-x}dx
tangent of 4x^2-6x	tangent\:4x^{2}-6x
integral of e^{-x/a}	\int\:e^{-\frac{x}{a}}dx
integral from-1 to 0 of (x^5-4x^3+4x+4)	\int\:_{-1}^{0}(x^{5}-4x^{3}+4x+4)dx
integral of (4x^2-8x)/((x-1)^2(x^2+1))	\int\:\frac{4x^{2}-8x}{(x-1)^{2}(x^{2}+1)}dx
integral of xcos(npix/2)	\int\:x\cos(n\cdot\:π\cdot\:\frac{x}{2})dx
derivative of 1/(sqrt(2x-1))	\frac{d}{dx}(\frac{1}{\sqrt{2x-1}})
integral of (12x)/(2x-5)	\int\:\frac{12x}{2x-5}dx
limit as x approaches 0 of (csc(2x))/x	\lim\:_{x\to\:0}(\frac{\csc(2x)}{x})
derivative of (3x-5^7(5x+2)^4)	\frac{d}{dx}((3x-5)^{7}(5x+2)^{4})
(\partial)/(\partial x)(t^2e^{(x^2)/(4t)})	\frac{\partial\:}{\partial\:x}(t^{2}e^{\frac{x^{2}}{4t}})

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