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Popular Calculus Problems

area x+2y=7,x+8=y^2	area\:x+2y=7,x+8=y^{2}
integral of 14x^6y^{-4}-12x^5y^{-3}	\int\:14x^{6}y^{-4}-12x^{5}y^{-3}dx
limit as x approaches 3 of sqrt(12-x)-3	\lim\:_{x\to\:3}(\sqrt{12-x}-3)
limit as x approaches infinity of (1+(2/x))^{(x/4)}	\lim\:_{x\to\:\infty\:}((1+(\frac{2}{x}))^{(\frac{x}{4})})
integral from 0 to 3 of x^3-5x	\int\:_{0}^{3}x^{3}-5xdx
(dy)/(dx)= 1/7 sqrt(y)cos^2(sqrt(y))	\frac{dy}{dx}=\frac{1}{7}\sqrt{y}\cos^{2}(\sqrt{y})
(ysin(x)+xycos(x))dx+(xsin(x)+1)dy=0	(y\sin(x)+xy\cos(x))dx+(x\sin(x)+1)dy=0
limit as x approaches 0 of x/(e^x)	\lim\:_{x\to\:0}(\frac{x}{e^{x}})
limit as n approaches infinity of ln(n)	\lim\:_{n\to\:\infty\:}(\ln(n))
tangent of x^2+4/x-10,\at x=8	tangent\:x^{2}+\frac{4}{x}-10,\at\:x=8
slope of (-3,5),(-7,-9)	slope\:(-3,5),(-7,-9)
integral of (5x^3)/(sqrt(3+x^2))	\int\:\frac{5x^{3}}{\sqrt{3+x^{2}}}dx
integral of sqrt(x)-1	\int\:\sqrt{x}-1dx
tangent of y=((x-1)/(x+1))	tangent\:y=(\frac{x-1}{x+1})
(\partial)/(\partial x)(x^2y+2x^2-y-2)	\frac{\partial\:}{\partial\:x}(x^{2}y+2x^{2}-y-2)
limit as x approaches 0+of f(x)	\lim\:_{x\to\:0+}(f(x))
integral of (y^2)/(1+x^2)	\int\:\frac{y^{2}}{1+x^{2}}dx
laplacetransform f(t)=7t+3	laplacetransform\:f(t)=7t+3
integral of x/((x+2)(3x-1))	\int\:\frac{x}{(x+2)(3x-1)}dx
integral from 1 to 4 of 1/(sqrt(x-1))	\int\:_{1}^{4}\frac{1}{\sqrt{x-1}}dx
integral of ln(1-x)	\int\:\ln(1-x)dx
(dy)/(dt)=2(t+1)y,y(0)=1	\frac{dy}{dt}=2(t+1)y,y(0)=1
derivative of e^x-xe^x	\frac{d}{dx}(e^{x}-xe^{x})
integral from 1 to 2 of 3r^4ln(r)	\int\:_{1}^{2}3r^{4}\ln(r)dr
limit as x approaches 2 of sqrt(6x+13)	\lim\:_{x\to\:2}(\sqrt{6x+13})
integral of (3x)/(4-2x^2)	\int\:\frac{3x}{4-2x^{2}}dx
derivative of-(25000/(x^2)+10)	\frac{d}{dx}(-\frac{25000}{x^{2}}+10)
derivative of (4x^5+5/(x^3))	\frac{d}{dx}(\frac{4x^{5}+5}{x^{3}})
integral from 2 to 7 of 1/(sqrt(x^2-4))	\int\:_{2}^{7}\frac{1}{\sqrt{x^{2}-4}}dx
derivative of (25)/(t^2)-5/t	derivative\:\frac{25}{t^{2}}-\frac{5}{t}
derivative of xe^{2x}(arcsin(3x))	\frac{d}{dx}(xe^{2x}(\arcsin(3x)))
1200(dy)/(dx)=12000-200y-1800	1200\frac{dy}{dx}=12000-200y-1800
integral of (-2)/(x^6)	\int\:\frac{-2}{x^{6}}dx
tangent of f(x)=(7x)/(x+7),(3,2.1)	tangent\:f(x)=\frac{7x}{x+7},(3,2.1)
sum from n=1 to infinity of (1/3)^{n-1}	\sum\:_{n=1}^{\infty\:}(\frac{1}{3})^{n-1}
integral of xsqrt(144-x^2)	\int\:x\sqrt{144-x^{2}}dx
integral of 3xe-2x	\int\:3xe-2xdx
integral of (y^2-2y+4)/(y(y-2)^2)	\int\:\frac{y^{2}-2y+4}{y(y-2)^{2}}dy
y^{''''}-y^{''}=4x+2xe^{-x}	y^{\prime\:\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}=4x+2xe^{-x}
integral of (sin(3t))	\int\:(\sin(3t))dt
slope of (1.4)(7.1)	slope\:(1.4)(7.1)
integral from 3 to 9 of 1/(x(ln(x))^2)	\int\:_{3}^{9}\frac{1}{x(\ln(x))^{2}}dx
derivative of f(x)=(1-4x)/(3+x)	derivative\:f(x)=\frac{1-4x}{3+x}
limit as x approaches 5 of ln(x-4)+1/2	\lim\:_{x\to\:5}(\ln(x-4)+\frac{1}{2})
integral of none	\int\:nonedx
integral of (e^{1/(x^3)})/(x^4)	\int\:\frac{e^{\frac{1}{x^{3}}}}{x^{4}}dx
(\partial)/(\partial x)(8x^2cos(5)x^3)	\frac{\partial\:}{\partial\:x}(8x^{2}\cos(5)x^{3})
derivative of (ln(x)/(e^x))	\frac{d}{dx}(\frac{\ln(x)}{e^{x}})
integral from 0 to 2 of 1/(sqrt(9-x^2))	\int\:_{0}^{2}\frac{1}{\sqrt{9-x^{2}}}dx
derivative of f(x)=3x^4	derivative\:f(x)=3x^{4}
limit as x approaches 7 of (x^2-4)/(7-x)	\lim\:_{x\to\:7}(\frac{x^{2}-4}{7-x})
integral of arctan(5t)	\int\:\arctan(5t)dt
limit as x approaches 0 of (x^2+1)/(x^2)	\lim\:_{x\to\:0}(\frac{x^{2}+1}{x^{2}})
derivative of y= 1/(x(8+ln(x)))	derivative\:y=\frac{1}{x(8+\ln(x))}
xy^'+y=-3xy^2	xy^{\prime\:}+y=-3xy^{2}
integral of e^{-3x}cos(2x)	\int\:e^{-3x}\cos(2x)dx
(5x+2)+(5y-5)y^'=0	(5x+2)+(5y-5)y^{\prime\:}=0
tangent of (4x)/(x^2+1)(1.1)	tangent\:\frac{4x}{x^{2}+1}(1.1)
integral of (\sqrt[3]{x^8})	\int\:(\sqrt[3]{x^{8}})dx
integral of 1/(13x)	\int\:\frac{1}{13x}dx
integral of 9arctan(1/x)	\int\:9\arctan(\frac{1}{x})dx
limit as x approaches infinity of ln(x)+ln(1/(1/x+1))	\lim\:_{x\to\:\infty\:}(\ln(x)+\ln(\frac{1}{\frac{1}{x}+1}))
y^2(1-x^2)^{1/2}dy=arcsin(x)dx	y^{2}(1-x^{2})^{\frac{1}{2}}dy=\arcsin(x)dx
derivative of g(u)=(8u^2)/((u^2+u)^3)	derivative\:g(u)=\frac{8u^{2}}{(u^{2}+u)^{3}}
integral of-x^2-2x+3	\int\:-x^{2}-2x+3dx
integral of (2x+1)/(x^2+x+3)	\int\:\frac{2x+1}{x^{2}+x+3}dx
derivative of f(x)=(x^2-81)/(x-9)	derivative\:f(x)=\frac{x^{2}-81}{x-9}
integral of sin(12x)cos(3x)	\int\:\sin(12x)\cos(3x)dx
derivative of (x^2/((1-y^2)))	\frac{d}{dx}(\frac{x^{2}}{(1-y^{2})})
integral of ((y^2)/4)^2	\int\:(\frac{y^{2}}{4})^{2}dy
derivative of e^{x^3+6x^2}	\frac{d}{dx}(e^{x^{3}+6x^{2}})
integral of 1/(10(x+2))	\int\:\frac{1}{10(x+2)}dx
integral of 4cot^3(x)csc^3(x)	\int\:4\cot^{3}(x)\csc^{3}(x)dx
tangent of y=\sqrt[5]{2x^3+8x},(2,2)	tangent\:y=\sqrt[5]{2x^{3}+8x},(2,2)
limit as x approaches 0 of (sin(0))/0	\lim\:_{x\to\:0}(\frac{\sin(0)}{0})
area x^3-3x^2-9x+27,x+3	area\:x^{3}-3x^{2}-9x+27,x+3
limit as x approaches 2 of x^2+2x+3	\lim\:_{x\to\:2}(x^{2}+2x+3)
area y=4x+12,y=x^2	area\:y=4x+12,y=x^{2}
integral of 1/((x^2+6x+10)^2)	\int\:\frac{1}{(x^{2}+6x+10)^{2}}dx
derivative of y=5x^{10}e^x	derivative\:y=5x^{10}e^{x}
integral of xsin(4)x^2	\int\:x\sin(4)x^{2}dx
integral of sec^3(7x)tan^5(7x)	\int\:\sec^{3}(7x)\tan^{5}(7x)dx
laplacetransform f(t)=t^2-2t	laplacetransform\:f(t)=t^{2}-2t
y^{''''}+32y^{''}+256y=0	y^{\prime\:\prime\:\prime\:\prime\:}+32y^{\prime\:\prime\:}+256y=0
integral of (x^2-17x+4)/(x+7)	\int\:\frac{x^{2}-17x+4}{x+7}dx
derivative of x^2+4x-8	\frac{d}{dx}(x^{2}+4x-8)
limit as x approaches 0 of ((e^{3x}-1))/(sin(5x))	\lim\:_{x\to\:0}(\frac{(e^{3x}-1)}{\sin(5x)})
integral of cos^3(x)sin^3(x)	\int\:\cos^{3}(x)\sin^{3}(x)dx
y^{''}-81y=0	y^{\prime\:\prime\:}-81y=0
derivative of e^{2x+4}	derivative\:e^{2x+4}
derivative of (2x+3)/(3x-2)	derivative\:\frac{2x+3}{3x-2}
integral of (\sqrt[3]{2x+1})	\int\:(\sqrt[3]{2x+1})dx
limit as h approaches+0 of-(5h)/(x(x+h))	\lim\:_{h\to\:+0}(-\frac{5h}{x(x+h)})
derivative of-3/(1-3x)	\frac{d}{dx}(-\frac{3}{1-3x})
integral of (6000)/(6x+70)	\int\:\frac{6000}{6x+70}dx
integral of 3/(sqrt(16-9x^2))	\int\:\frac{3}{\sqrt{16-9x^{2}}}dx
derivative of y= x/(x+b/x)	derivative\:y=\frac{x}{x+\frac{b}{x}}
taylor 1/((1+x)^3),0	taylor\:\frac{1}{(1+x)^{3}},0
inverse oflaplace 3/(s^2+9)	inverselaplace\:\frac{3}{s^{2}+9}
tangent of h(x)= 9/x ,\at x=2	tangent\:h(x)=\frac{9}{x},\at\:x=2

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