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Popular Calculus Problems

(dy)/(dx)=x(y-1)^2	\frac{dy}{dx}=x(y-1)^{2}
tangent of y=(x^3-16x)^{10},(4,0)	tangent\:y=(x^{3}-16x)^{10},(4,0)
limit as x approaches 0 of e^x-1/x	\lim\:_{x\to\:0}(e^{x}-\frac{1}{x})
integral from 0 to 5 of e^{-2x}	\int\:_{0}^{5}e^{-2x}dx
f(x)= 2/(x-3)	f(x)=\frac{2}{x-3}
(x^2-3y^2)dx+2xydy=0	(x^{2}-3y^{2})dx+2xydy=0
limit as x approaches pi of sin(11/6 x)	\lim\:_{x\to\:π}(\sin(\frac{11}{6}x))
integral of sin^5(7x)	\int\:\sin^{5}(7x)dx
(dy)/(dx)=32x^3y^3	\frac{dy}{dx}=32x^{3}y^{3}
limit as x approaches 0 of (1-1/(2x))^x	\lim\:_{x\to\:0}((1-\frac{1}{2x})^{x})
d/(dy)(ye^x+2e^x+y^2)	\frac{d}{dy}(ye^{x}+2e^{x}+y^{2})
integral of sqrt((2x+1)^5)	\int\:\sqrt{(2x+1)^{5}}dx
inverse oflaplace (-2)/((s^2+1)^2)	inverselaplace\:\frac{-2}{(s^{2}+1)^{2}}
integral from 0 to pi of sin^4(3t)	\int\:_{0}^{π}\sin^{4}(3t)dt
integral of 40x^3+20	\int\:40x^{3}+20dx
integral of 20-sqrt((20)^2-x^2)	\int\:20-\sqrt{(20)^{2}-x^{2}}dx
integral of (4x^3+3^x)	\int\:(4x^{3}+3^{x})dx
integral of ((e^x-2)e^x)/(e^x+1)	\int\:\frac{(e^{x}-2)e^{x}}{e^{x}+1}dx
(d^2)/(dx^2)(sqrt(x))	\frac{d^{2}}{dx^{2}}(\sqrt{x})
area sqrt(x),-x,1,4	area\:\sqrt{x},-x,1,4
derivative of sin(2x)	derivative\:\sin(2x)
integral of x+(x^2)/2+(5x^3)/3	\int\:x+\frac{x^{2}}{2}+\frac{5x^{3}}{3}dx
integral from 0 to infinity of 5/(x^2+1)	\int\:_{0}^{\infty\:}\frac{5}{x^{2}+1}dx
integral of 1/(x-8)	\int\:\frac{1}{x-8}dx
sum from n=1 to infinity of (cos(29))^n	\sum\:_{n=1}^{\infty\:}(\cos(29))^{n}
(d^2)/(dx^2)(1/(3+x))	\frac{d^{2}}{dx^{2}}(\frac{1}{3+x})
derivative of f(x)=(x^2+3)^4	derivative\:f(x)=(x^{2}+3)^{4}
integral of 1/((1-x)^3sqrt(x^2-2x-1))	\int\:\frac{1}{(1-x)^{3}\sqrt{x^{2}-2x-1}}dx
derivative of \sqrt[3]{x}+2sqrt(x^3)	derivative\:\sqrt[3]{x}+2\sqrt{x^{3}}
5(dx)/(dt)+10x=120sin(60t)	5\frac{dx}{dt}+10x=120\sin(60t)
tangent of f(x)= 1/(x-2),\at x=6	tangent\:f(x)=\frac{1}{x-2},\at\:x=6
integral of 1/(2sin(x)-cos(x)+5)	\int\:\frac{1}{2\sin(x)-\cos(x)+5}dx
derivative of (sqrt(5)^x)	\frac{d}{dx}((\sqrt{5})^{x})
(2sqrt(t^2+1))^'	(2\sqrt{t^{2}+1})^{\prime\:}
derivative of 14e^x	\frac{d}{dx}(14e^{x})
integral of arccot(3x)	\int\:\arccot(3x)dx
y^'+y=6	y^{\prime\:}+y=6
tangent of y= x/(x+3),(1,2)	tangent\:y=\frac{x}{x+3},(1,2)
derivative of 3x^2+3	\frac{d}{dx}(3x^{2}+3)
tangent of 6/(sqrt(x))	tangent\:\frac{6}{\sqrt{x}}
sum from n=1 to infinity of n^{-2/3}	\sum\:_{n=1}^{\infty\:}n^{-\frac{2}{3}}
laplacetransform 2(t-3)^2+9(t-3)+11	laplacetransform\:2(t-3)^{2}+9(t-3)+11
derivative of y=3e^{4x}+6e^{2x}	derivative\:y=3e^{4x}+6e^{2x}
derivative of e^{7x}+e^{-7x}	\frac{d}{dx}(e^{7x}+e^{-7x})
derivative of 1+(3/2 x^{(1/2})^2)	\frac{d}{dx}(1+(\frac{3}{2}x^{(\frac{1}{2})})^{2})
tangent of f(x)=20x-16x^2,\at x=3	tangent\:f(x)=20x-16x^{2},\at\:x=3
(\partial)/(\partial x)(v/(2u+v))	\frac{\partial\:}{\partial\:x}(\frac{v}{2u+v})
derivative of 3e^{-3x}	\frac{d}{dx}(3e^{-3x})
inverse oflaplace (5s+50.1)/((s+5)^2-5)	inverselaplace\:\frac{5s+50.1}{(s+5)^{2}-5}
sum from k=0 to infinity of (k-1)/(2^{k+1)}	\sum\:_{k=0}^{\infty\:}\frac{k-1}{2^{k+1}}
limit as (x,y) approaches (1,2) of 1+x+y	\lim\:_{(x,y)\to\:(1,2)}(1+x+y)
f(x)=x^3-5+2x	f(x)=x^{3}-5+2x
limit as x approaches infinity of e^{-x}	\lim\:_{x\to\:\infty\:}(e^{-x})
(\partial)/(\partial x)((2x-3)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{2x-3}{xy})
derivative of sqrt(7-3u)	derivative\:\sqrt{7-3u}
(\partial)/(\partial y)(x^2y+3y+x^2y^3-4x)	\frac{\partial\:}{\partial\:y}(x^{2}y+3y+x^{2}y^{3}-4x)
y^{''}+y^'-2y=2t,y(0)=0,y^'(0)=7	y^{\prime\:\prime\:}+y^{\prime\:}-2y=2t,y(0)=0,y^{\prime\:}(0)=7
tangent of y=x^3-2x+2(2.6)	tangent\:y=x^{3}-2x+2(2.6)
derivative of x+2/(sin(x))	\frac{d}{dx}(x+\frac{2}{\sin(x)})
integral from 0 to pi/2 of 24x^2sin(x)	\int\:_{0}^{\frac{π}{2}}24x^{2}\sin(x)dx
limit as x approaches 0-of 3/(x^2-x)	\lim\:_{x\to\:0-}(\frac{3}{x^{2}-x})
integral of (-x-8)/(x^2+9)	\int\:\frac{-x-8}{x^{2}+9}dx
integral of 15arctan(x)	\int\:15\arctan(x)dx
integral of (ln(x^{14}))/x	\int\:\frac{\ln(x^{14})}{x}dx
(\partial)/(\partial x)(-y^3-x)	\frac{\partial\:}{\partial\:x}(-y^{3}-x)
integral of sin^3(x/2)cos(x/2)	\int\:\sin^{3}(\frac{x}{2})\cos(\frac{x}{2})dx
derivative of f(x)=13	derivative\:f(x)=13
integral of (1+u)/(-2u-1-u^2)	\int\:\frac{1+u}{-2u-1-u^{2}}du
laplacetransform e^{-t}cos^2(t)	laplacetransform\:e^{-t}\cos^{2}(t)
integral of (x^2+8x-3)/(x^3+3x)	\int\:\frac{x^{2}+8x-3}{x^{3}+3x}dx
y^{''}+5y^'+6y=108x^2	y^{\prime\:\prime\:}+5y^{\prime\:}+6y=108x^{2}
integral from 7 to infinity of (ln(x))/x	\int\:_{7}^{\infty\:}\frac{\ln(x)}{x}dx
integral of (\sqrt[9]{x})	\int\:(\sqrt[9]{x})dx
integral of 9x^{-3}	\int\:9x^{-3}dx
derivative of (2x/(7x^2+1))	\frac{d}{dx}(\frac{2x}{7x^{2}+1})
y^{''}+256y=sec(16x)	y^{\prime\:\prime\:}+256y=\sec(16x)
tangent of y=12(x-1/x)^2,\at x=2	tangent\:y=12(x-\frac{1}{x})^{2},\at\:x=2
derivative of y=4xcos(x^2)	derivative\:y=4x\cos(x^{2})
integral of (2e^{9x})	\int\:(2e^{9x})dx
derivative of ((x-1)/((x-2)))	\frac{d}{dx}(\frac{(x-1)}{(x-2)})
integral of x^5e^{3x}	\int\:x^{5}e^{3x}dx
derivative of f(x)=(x+3)^2	derivative\:f(x)=(x+3)^{2}
integral from 1/2 to 1 of (x^{-3}-2)	\int\:_{\frac{1}{2}}^{1}(x^{-3}-2)dx
tangent of y=6xe^x,(0,0)	tangent\:y=6xe^{x},(0,0)
derivative of cos(4t)	derivative\:\cos(4t)
(\partial)/(\partial x)(e^{-y}(x+e^y))	\frac{\partial\:}{\partial\:x}(e^{-y}(x+e^{y}))
3x^2y^'=y^'+6xe^{-y}	3x^{2}y^{\prime\:}=y^{\prime\:}+6xe^{-y}
derivative of (e^{4x^2})^7	derivative\:(e^{4x^{2}})^{7}
(dx)/(dt)=5x-3	\frac{dx}{dt}=5x-3
derivative of 12x	derivative\:12x
y^'=e^{3y}sin(4x)	y^{\prime\:}=e^{3y}\sin(4x)
(\partial)/(\partial x)(sqrt(6-x^2-y^2))	\frac{\partial\:}{\partial\:x}(\sqrt{6-x^{2}-y^{2}})
tangent of f(x)=x^3-5x^2	tangent\:f(x)=x^{3}-5x^{2}
integral from-2 to 0 of x^2e^{x^3+8}	\int\:_{-2}^{0}x^{2}e^{x^{3}+8}dx
integral of 2/(1+cos(2x))	\int\:\frac{2}{1+\cos(2x)}dx
integral of (arctan(x))/(x^2+1)	\int\:\frac{\arctan(x)}{x^{2}+1}dx
taylor e^x,2	taylor\:e^{x},2
integral of (ax+b)/(cx+	\int\:\frac{ax+b}{cx+d}dx
derivative of (4x^{3/2}/x)	\frac{d}{dx}(\frac{4x^{\frac{3}{2}}}{x})
integral of 10x-3x^2-x^3	\int\:10x-3x^{2}-x^{3}dx

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