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Popular Calculus Problems

x(dy)/(dx)-3y=x^3	x\frac{dy}{dx}-3y=x^{3}
limit as x approaches 3+of x/(x^2-4x+3)	\lim\:_{x\to\:3+}(\frac{x}{x^{2}-4x+3})
limit as x approaches-1 of 3x^2+3x^3+10	\lim\:_{x\to\:-1}(3x^{2}+3x^{3}+10)
area 5/2 sin((pix)/3), 5/3 x,[0,1.5]	area\:\frac{5}{2}\sin(\frac{πx}{3}),\frac{5}{3}x,[0,1.5]
area y=2x,y=x^2	area\:y=2x,y=x^{2}
integral of (x^2+1)^{-2}	\int\:(x^{2}+1)^{-2}dx
area y=x^2-9,y=-x+5,x=0,x=2	area\:y=x^{2}-9,y=-x+5,x=0,x=2
tangent of f(x)=x^2-7x+7,7,\at x=0	tangent\:f(x)=x^{2}-7x+7,7,\at\:x=0
d/(dθ)(cot(ln(θ-cos(sqrt(θ)))))	\frac{d}{dθ}(\cot(\ln(θ-\cos(\sqrt{θ}))))
derivative of log_{3}(e^{7x})	derivative\:\log_{3}(e^{7x})
laplacetransform t^2e^{,\at}	laplacetransform\:t^{2}e^{,\at\:}
(\partial)/(\partial x)(3x^3+4x^2y-4y^3)	\frac{\partial\:}{\partial\:x}(3x^{3}+4x^{2}y-4y^{3})
derivative of 5ln(sec(x+tan(x)))	\frac{d}{dx}(5\ln(\sec(x)+\tan(x)))
integral of ((arctan(x))^2)/(1+x^2)	\int\:\frac{(\arctan(x))^{2}}{1+x^{2}}dx
yy^'+xy^2=(e^{-x^2})	yy^{\prime\:}+xy^{2}=(e^{-x^{2}})
tangent of f(x)= 1/3 x^3+5.5x^2+30x+22	tangent\:f(x)=\frac{1}{3}x^{3}+5.5x^{2}+30x+22
limit as x approaches 0+of (x^x-1)/(2x)	\lim\:_{x\to\:0+}(\frac{x^{x}-1}{2x})
limit as t approaches 0 of 1+t^3	\lim\:_{t\to\:0}(1+t^{3})
integral of 1/12 cot(3x)	\int\:\frac{1}{12}\cot(3x)dx
derivative of sqrt(15)	derivative\:\sqrt{15}
limit as x approaches 5 of 2x^2+3x-7	\lim\:_{x\to\:5}(2x^{2}+3x-7)
derivative of (sin(x^2+y^2)/(x^2+y^2))	\frac{d}{dx}(\frac{\sin(x^{2}+y^{2})}{x^{2}+y^{2}})
integral of sqrt((4-x^2))	\int\:\sqrt{(4-x^{2})}dx
d/(dt)(cos(t)sin(t))	\frac{d}{dt}(\cos(t)\sin(t))
(\partial)/(\partial x)(x/((x^2+y^2)))	\frac{\partial\:}{\partial\:x}(\frac{x}{(x^{2}+y^{2})})
integral of 7x(8-x)	\int\:7x(8-x)dx
area y^2=4+x,y^2+x=2	area\:y^{2}=4+x,y^{2}+x=2
derivative of f(x)=(1+2x^2)^2+2x^3	derivative\:f(x)=(1+2x^{2})^{2}+2x^{3}
integral from 0 to 1 of sqrt(1+x^3)	\int\:_{0}^{1}\sqrt{1+x^{3}}dx
derivative of arcsin(x+xsqrt(1-x^2))	\frac{d}{dx}(\arcsin(x)+x\sqrt{1-x^{2}})
derivative of 4x^2+4x^3	\frac{d}{dx}(4x^{2}+4x^{3})
integral of e^{-x}cos(7x)	\int\:e^{-x}\cos(7x)dx
derivative of ln(1+6x)	\frac{d}{dx}(\ln(1+6x))
(e^{-y}+1)sin(x)dx=(1+cos(x))dy,y(0)=0	(e^{-y}+1)\sin(x)dx=(1+\cos(x))dy,y(0)=0
integral of p(p+1)^5	\int\:p(p+1)^{5}dp
(\partial)/(\partial y)(y-1/(x^2))	\frac{\partial\:}{\partial\:y}(y-\frac{1}{x^{2}})
integral of tan(x)sqrt(sec(x))	\int\:\tan(x)\sqrt{\sec(x)}dx
(dy)/(dt)=e^{-t}	\frac{dy}{dt}=e^{-t}
(\partial)/(\partial y)(2xz)	\frac{\partial\:}{\partial\:y}(2xz)
derivative of e^{-4}	derivative\:e^{-4}
tangent of y=sqrt(x+3),(1,2)	tangent\:y=\sqrt{x+3},(1,2)
derivative of sin(x)+7/5 cot(x)	derivative\:\sin(x)+\frac{7}{5}\cot(x)
area x^2=y+1,x+y=1	area\:x^{2}=y+1,x+y=1
derivative of cos(pi/x)	derivative\:\cos(\frac{π}{x})
integral of y/x+4x	\int\:\frac{y}{x}+4xdx
integral from-1 to 2 of 1	\int\:_{-1}^{2}1
integral of 6/(5x^2)	\int\:\frac{6}{5x^{2}}dx
inverse oflaplace e^{-2t}	inverselaplace\:e^{-2t}
integral of xcos(3x+2)	\int\:x\cos(3x+2)dx
derivative of-1/(ln(2)x^2)	derivative\:-\frac{1}{\ln(2)x^{2}}
integral of ln(5+x)	\int\:\ln(5+x)dx
derivative of ax*ln(ax^2+3)	\frac{d}{dx}(ax\cdot\:\ln(ax^{2}+3))
integral of (cos(x))/(sin^3(x))	\int\:\frac{\cos(x)}{\sin^{3}(x)}dx
integral of sqrt((x+1)/x)	\int\:\sqrt{\frac{x+1}{x}}dx
(\partial}{\partial x}(\frac{x-y)/x)	\frac{\partial\:}{\partial\:x}(\frac{x-y}{x})
derivative of ln(x/4 (x-4))	\frac{d}{dx}(\ln(\frac{x}{4})(x-4))
integral of (sin(x))/(cot(x))	\int\:\frac{\sin(x)}{\cot(x)}dx
inverse oflaplace s/(s^2-16)	inverselaplace\:\frac{s}{s^{2}-16}
y^'=x^2-y-2,y(0)=1	y^{\prime\:}=x^{2}-y-2,y(0)=1
integral of (x^2)/((x^2-2x+2)^2)	\int\:\frac{x^{2}}{(x^{2}-2x+2)^{2}}dx
derivative of ln(7x^3)	\frac{d}{dx}(\ln(7x^{3}))
(x^2+y+y^2)dx=xdy	(x^{2}+y+y^{2})dx=xdy
integral of 216sin(9x)\sqrt[3]{cos(9x)}	\int\:216\sin(9x)\sqrt[3]{\cos(9x)}dx
derivative of y=x+sqrt(x)	derivative\:y=x+\sqrt{x}
derivative of 2x^pi	derivative\:2x^{π}
integral of (2x+5)^{10}	\int\:(2x+5)^{10}dx
derivative of sqrt(1+cos(x))	\frac{d}{dx}(\sqrt{1+\cos(x)})
derivative of e^{2x}*ln(3x)	\frac{d}{dx}(e^{2x}\cdot\:\ln(3x))
(dy}{dx}-\frac{6y)/x =x^6e^x	\frac{dy}{dx}-\frac{6y}{x}=x^{6}e^{x}
(\partial)/(\partial x)(x^5y^8+3x^9y)	\frac{\partial\:}{\partial\:x}(x^{5}y^{8}+3x^{9}y)
derivative of (0.1x/((x+3)^2))	\frac{d}{dx}(\frac{0.1x}{(x+3)^{2}})
d/(du)(u^2-v^2)	\frac{d}{du}(u^{2}-v^{2})
(\partial)/(\partial y)(2xsin(xy))	\frac{\partial\:}{\partial\:y}(2x\sin(xy))
integral of 2x(3x-2)^6	\int\:2x(3x-2)^{6}dx
slope of (5,9),(4,5)	slope\:(5,9),(4,5)
taylor x^{1/3},x=8	taylor\:x^{\frac{1}{3}},x=8
limit as x approaches 0 of (-x^3)/(x^2)	\lim\:_{x\to\:0}(\frac{-x^{3}}{x^{2}})
tangent of f(x)=ax^2,\at x=-2	tangent\:f(x)=ax^{2},\at\:x=-2
integral of (2x^3+3x^2+x+1)/(2x+1)	\int\:\frac{2x^{3}+3x^{2}+x+1}{2x+1}dx
area y=2x+5,y=15-x^2,x=-1,x=2	area\:y=2x+5,y=15-x^{2},x=-1,x=2
integral of (4+3x)^5	\int\:(4+3x)^{5}dx
integral of x/((1-x^2)^3)	\int\:\frac{x}{(1-x^{2})^{3}}dx
taylor x^{2/3},1	taylor\:x^{\frac{2}{3}},1
tangent of y=(x^3+1)(3x^2-4x+2),(1,2)	tangent\:y=(x^{3}+1)(3x^{2}-4x+2),(1,2)
derivative of (1/(y^2)-8/(y^4))(y+2y^3)	derivative\:(\frac{1}{y^{2}}-\frac{8}{y^{4}})(y+2y^{3})
inverse oflaplace 5/(s^2+1)	inverselaplace\:\frac{5}{s^{2}+1}
derivative of (sqrt(x)+1/(sqrt(x^3))^2)	\frac{d}{dx}((\sqrt{x}+\frac{1}{\sqrt{x^{3}}})^{2})
integral of ((x^2+1)/(x^3+3x))	\int\:(\frac{x^{2}+1}{x^{3}+3x})dx
derivative of y=(4x^2+8x+4)/(sqrt(x))	derivative\:y=\frac{4x^{2}+8x+4}{\sqrt{x}}
limit as x approaches 5 of 5-x	\lim\:_{x\to\:5}(5-x)
sum from k=0 to infinity of 1/2*(-1)^k	\sum\:_{k=0}^{\infty\:}\frac{1}{2}\cdot\:(-1)^{k}
(\partial)/(\partial x)(1/(1+x^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{1+x^{2}})
limit as x approaches 1 of 1^{1/(1-x)}	\lim\:_{x\to\:1}(1^{\frac{1}{1-x}})
(\partial)/(\partial u)(u+vw)	\frac{\partial\:}{\partial\:u}(u+vw)
integral of cos^7(x)*sin^3(x)	\int\:\cos^{7}(x)\cdot\:\sin^{3}(x)dx
integral of ((y+1))/((y-1))	\int\:\frac{(y+1)}{(y-1)}dy
integral of 6x^5-18x^2+7	\int\:6x^{5}-18x^{2}+7dx
dx=xsqrt(x^2-16)dy	dx=x\sqrt{x^{2}-16}dy
limit as x approaches 20 of sqrt(10)	\lim\:_{x\to\:20}(\sqrt{10})
integral of ((4+x^7)^67x^6)	\int\:((4+x^{7})^{6}7x^{6})dx

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