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Popular Calculus Problems

x(dy)/(dx)-2y=2	x\frac{dy}{dx}-2y=2
derivative of 400(15-x^2(3x-2))	\frac{d}{dx}(400(15-x^{2})(3x-2))
integral of cos(bx)	\int\:\cos(bx)dx
derivative of (x^2/(arccos(x^2)))	\frac{d}{dx}(\frac{x^{2}}{\arccos(x^{2})})
integral of (x^2)/((25-x^2)^{3/2)}	\int\:\frac{x^{2}}{(25-x^{2})^{\frac{3}{2}}}dx
laplacetransform 2t+1	laplacetransform\:2t+1
5y^{''}-6y^'+3y=2-3x^2	5y^{\prime\:\prime\:}-6y^{\prime\:}+3y=2-3x^{2}
derivative of y=(x^5)/(5-x^4)	derivative\:y=\frac{x^{5}}{5-x^{4}}
derivative of 64-x^2	\frac{d}{dx}(64-x^{2})
derivative of e^{7x}cos(10x)	derivative\:e^{7x}\cos(10x)
derivative of sin^2(2x^3+3x)	\frac{d}{dx}(\sin^{2}(2x^{3}+3x))
derivative of y=sqrt(-2x^2+24)	derivative\:y=\sqrt{-2x^{2}+24}
integral from 0 to 1 of e^x(e^x-1)	\int\:_{0}^{1}e^{x}(e^{x}-1)dx
laplacetransform 30t^2	laplacetransform\:30t^{2}
limit as x approaches infinity of-ln(x)	\lim\:_{x\to\:\infty\:}(-\ln(x))
integral of (4x)/(sqrt(x^2-16))	\int\:\frac{4x}{\sqrt{x^{2}-16}}dx
area y=x^2,y=x	area\:y=x^{2},y=x
integral from 0 to pi/6 of 6sec^2(x)	\int\:_{0}^{\frac{π}{6}}6\sec^{2}(x)dx
derivative of sin(7x+cos(6x))	\frac{d}{dx}(\sin(7x)+\cos(6x))
(dx)/(dt)= 3/(xe^{t+3x)}	\frac{dx}{dt}=\frac{3}{xe^{t+3x}}
integral of-x^2-x+2	\int\:-x^{2}-x+2dx
derivative of sqrt(cos(3x-1))	\frac{d}{dx}(\sqrt{\cos(3x-1)})
y^{''}+4y=0,y(0)=5,y^'(0)=1	y^{\prime\:\prime\:}+4y=0,y(0)=5,y^{\prime\:}(0)=1
integral from 0 to s of 1/(0.2s+10)	\int\:_{0}^{s}\frac{1}{0.2s+10}ds
(\partial)/(\partial x)(3x^2-4xy+xyz)	\frac{\partial\:}{\partial\:x}(3x^{2}-4xy+xyz)
y^'=x^2-2	y^{\prime\:}=x^{2}-2
integral of (4sqrt(x))/(x-1)	\int\:\frac{4\sqrt{x}}{x-1}dx
y^'=5ty^2	y^{\prime\:}=5ty^{2}
derivative of 9x^{-2}	derivative\:9x^{-2}
derivative of y= x/(1-ln(x-5))	derivative\:y=\frac{x}{1-\ln(x-5)}
derivative of (xcos(x+pi)/(x-pi))	\frac{d}{dx}(\frac{x\cos(x)+π}{x-π})
limit as x approaches 0 of (1-e^{4x})^x	\lim\:_{x\to\:0}((1-e^{4x})^{x})
derivative of sin^3(cos(2x))	\frac{d}{dx}(\sin^{3}(\cos(2x)))
integral of 1/(25+x^2)	\int\:\frac{1}{25+x^{2}}dx
(1+y)dy=2tdt	(1+y)dy=2tdt
integral of (x^2)/(sqrt(16-x^2))	\int\:\frac{x^{2}}{\sqrt{16-x^{2}}}dx
derivative of \sqrt[3]{1+x}	derivative\:\sqrt[3]{1+x}
derivative of sqrt(x)+sqrt(y)	derivative\:\sqrt{x}+\sqrt{y}
limit as x approaches (3pi)/2 of cos(x)	\lim\:_{x\to\:\frac{3π}{2}}(\cos(x))
integral from 2 to 5 of 1/(x-2)	\int\:_{2}^{5}\frac{1}{x-2}dx
integral of e^{4x}cos(x)	\int\:e^{4x}\cos(x)dx
(dx}{dy}=\frac{x+y)/y	\frac{dx}{dy}=\frac{x+y}{y}
integral of-3x^4+x^3+5-5e^x	\int\:-3x^{4}+x^{3}+5-5e^{x}dx
integral of (1/(2x+1))	\int\:(\frac{1}{2x+1})dx
tangent of f(x)=3x^2-1,\at x=-2	tangent\:f(x)=3x^{2}-1,\at\:x=-2
integral of 5cos(5x)-4	\int\:5\cos(5x)-4dx
7y^{''}+30y=0	7y^{\prime\:\prime\:}+30y=0
derivative of f(x)=2x^2-x-3	derivative\:f(x)=2x^{2}-x-3
integral of 3t^{-1}	\int\:3t^{-1}dt
derivative of arccos(x/5)	\frac{d}{dx}(\arccos(\frac{x}{5}))
derivative of x/(x^2+13x+40)	derivative\:\frac{x}{x^{2}+13x+40}
integral of sqrt(16+x^2)	\int\:\sqrt{16+x^{2}}dx
integral from 1 to 22 of 1	\int\:_{1}^{22}1dx
integral of 8x^2cos(5x)	\int\:8x^{2}\cos(5x)dx
limit as x approaches 2+of x/(\|x\|)	\lim\:_{x\to\:2+}(\frac{x}{\left\|x\right\|})
slope of (-45)(-4-8)	slope\:(-45)(-4-8)
integral of e^{5x}sin(7x)	\int\:e^{5x}\sin(7x)dx
derivative of y=7x^{-3}	derivative\:y=7x^{-3}
inverse oflaplace (s+1)/(s^2+25)	inverselaplace\:\frac{s+1}{s^{2}+25}
f(x)=sqrt(1+2e^{3x)}	f(x)=\sqrt{1+2e^{3x}}
(d^2y)/(dx^2)y+81y=0	\frac{d^{2}y}{dx^{2}}y+81y=0
y^'=kx	y^{\prime\:}=kx
limit as x approaches infinity of 4x+7	\lim\:_{x\to\:\infty\:}(4x+7)
limit as n approaches infinity of (n^{100})/(50^n)	\lim\:_{n\to\:\infty\:}(\frac{n^{100}}{50^{n}})
derivative of sec(arctan(x))	\frac{d}{dx}(\sec(\arctan(x)))
derivative of ln(ln(x/(2-x^2)))	derivative\:\ln(\ln(\frac{x}{2-x^{2}}))
limit as x approaches 5 of x^2-3x-10	\lim\:_{x\to\:5}(x^{2}-3x-10)
(dy)/(dx)=5xy	\frac{dy}{dx}=5xy
(\partial)/(\partial x)(y^2-2xy-2x^2)	\frac{\partial\:}{\partial\:x}(y^{2}-2xy-2x^{2})
derivative of f(x)=sqrt(5x+7)	derivative\:f(x)=\sqrt{5x+7}
((x^2+1)/(x^2-1))^'	(\frac{x^{2}+1}{x^{2}-1})^{\prime\:}
limit as x approaches 2.99 of sqrt(1+x)	\lim\:_{x\to\:2.99}(\sqrt{1+x})
integral of 1/(sqrt(1+\sqrt{1+x))}	\int\:\frac{1}{\sqrt{1+\sqrt{1+x}}}dx
derivative of 3x^2-6	derivative\:3x^{2}-6
integral of (x-1)^2e^x	\int\:(x-1)^{2}e^{x}dx
(y^4-2xy)dx+3x^2dy=0	(y^{4}-2xy)dx+3x^{2}dy=0
(dy)/(dx)=(8e^{4x})/(2cos(2y))	\frac{dy}{dx}=\frac{8e^{4x}}{2\cos(2y)}
taylor 1/(3x+5)	taylor\:\frac{1}{3x+5}
(\partial)/(\partial y)(x-1/(y^2))	\frac{\partial\:}{\partial\:y}(x-\frac{1}{y^{2}})
inverse oflaplace 1/((s^2+s+1))	inverselaplace\:\frac{1}{(s^{2}+s+1)}
limit as x approaches 5 of sqrt(4x-3)	\lim\:_{x\to\:5}(\sqrt{4x-3})
derivative of 6/(4x+1)	derivative\:\frac{6}{4x+1}
longdivision (x^2-5x)/(x+1)	longdivision\:\frac{x^{2}-5x}{x+1}
laplacetransform (t-2)^3(t-2)	laplacetransform\:(t-2)^{3}(t-2)
y^'=((x^3-2y))/x	y^{\prime\:}=\frac{(x^{3}-2y)}{x}
derivative of 6sin(2x-3cos(3x))	\frac{d}{dx}(6\sin(2x)-3\cos(3x))
derivative of-536870912sin(2x)	\frac{d}{dx}(-536870912\sin(2x))
derivative of f(x)=sqrt(10+x)	derivative\:f(x)=\sqrt{10+x}
integral from 2 to 9 of 4/(8x-9)	\int\:_{2}^{9}\frac{4}{8x-9}dx
integral of (2x)/(sqrt(-5-6x^2-x^4))	\int\:\frac{2x}{\sqrt{-5-6x^{2}-x^{4}}}dx
derivative of (7x)/(8-tan(x))	derivative\:\frac{7x}{8-\tan(x)}
integral of (4x^2+x+4)/((x^2+1)^2)	\int\:\frac{4x^{2}+x+4}{(x^{2}+1)^{2}}dx
((3y^2-t^2))/((y^5))*y^'+t/((2y^4))=0,y(1)=3	\frac{(3y^{2}-t^{2})}{(y^{5})}\cdot\:y^{\prime\:}+\frac{t}{(2y^{4})}=0,y(1)=3
integral of 1/(1-sin(θ)+cos(θ))	\int\:\frac{1}{1-\sin(θ)+\cos(θ)}dθ
integral of 3e^{4t}	\int\:3e^{4t}dt
integral of tan^8(x)cos^9(x)	\int\:\tan^{8}(x)\cos^{9}(x)dx
derivative of y=10^x	derivative\:y=10^{x}
integral from 0 to 1 of x(1-sqrt(x))^2	\int\:_{0}^{1}x(1-\sqrt{x})^{2}dx
limit as x approaches 0 of x(1/x)	\lim\:_{x\to\:0}(x(\frac{1}{x}))
limit as x approaches 8 of 6/(x-8)	\lim\:_{x\to\:8}(\frac{6}{x-8})

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