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Popular Calculus Problems

integral of 5e^{-2x}+4	\int\:5e^{-2x}+4dx
6(dy)/(dx)-y^2=0	6\frac{dy}{dx}-y^{2}=0
laplacetransform 2cos(t)	laplacetransform\:2\cos(t)
2x^2y^{''}+5xy^'+y=x^2-x	2x^{2}y^{\prime\:\prime\:}+5xy^{\prime\:}+y=x^{2}-x
inverse oflaplace s/((s^2+2s+2))	inverselaplace\:\frac{s}{(s^{2}+2s+2)}
y^'-1/t y=0	y^{\prime\:}-\frac{1}{t}y=0
(dy)/(dx)=x(7-y)	\frac{dy}{dx}=x(7-y)
sum from n=0 to infinity of sin(pin)	\sum\:_{n=0}^{\infty\:}\sin(πn)
derivative of (-4x)/((x^2-1)^2)	derivative\:\frac{-4x}{(x^{2}-1)^{2}}
tangent of y= x/(1+x^2),(2, 2/5)	tangent\:y=\frac{x}{1+x^{2}},(2,\frac{2}{5})
tangent of f(x)=sqrt(x+3)	tangent\:f(x)=\sqrt{x+3}
(dy)/(dt)=(3-2y)*t^3	\frac{dy}{dt}=(3-2y)\cdot\:t^{3}
(\partial)/(\partial z)(-5z)	\frac{\partial\:}{\partial\:z}(-5z)
y^'=8y	y^{\prime\:}=8y
derivative of ln(1+4/x)	\frac{d}{dx}(\ln(1+\frac{4}{x}))
y^'=(y^2-1)x	y^{\prime\:}=(y^{2}-1)x
derivative of (x^2+3/(x^2-9x))	\frac{d}{dx}(\frac{x^{2}+3}{x^{2}-9x})
derivative of (ln(2x)/(2x))	\frac{d}{dx}(\frac{\ln(2x)}{2x})
(\partial)/(\partial u)(u*sin(v))	\frac{\partial\:}{\partial\:u}(u\cdot\:\sin(v))
integral from-2 to 1 of 1/(sqrt(2-x))	\int\:_{-2}^{1}\frac{1}{\sqrt{2-x}}dx
derivative of xe^{-6x}	\frac{d}{dx}(xe^{-6x})
derivative of tan(e^{5t})+e^{tan(5t)}	derivative\:\tan(e^{5t})+e^{\tan(5t)}
sum from k=2 to infinity of 3/(2^k)	\sum\:_{k=2}^{\infty\:}\frac{3}{2^{k}}
(\partial)/(\partial y)(e^{2x-3y})	\frac{\partial\:}{\partial\:y}(e^{2x-3y})
(\partial)/(\partial x)(y^2+x)	\frac{\partial\:}{\partial\:x}(y^{2}+x)
integral of e^{500x}	\int\:e^{500x}dx
derivative of sin(5)	\frac{d}{dx}(\sin(5))
(\partial)/(\partial x)(x^{5y})	\frac{\partial\:}{\partial\:x}(x^{5y})
derivative of f(x)= 8/x	derivative\:f(x)=\frac{8}{x}
derivative of ln(x^4sin^2(x))	\frac{d}{dx}(\ln(x^{4}\sin^{2}(x)))
(\partial)/(\partial x)(2x^4)	\frac{\partial\:}{\partial\:x}(2x^{4})
(\partial)/(\partial x)(12x+6y-x^2+xy-y^2)	\frac{\partial\:}{\partial\:x}(12x+6y-x^{2}+xy-y^{2})
tangent of sqrt(7x-6)	tangent\:\sqrt{7x-6}
(\partial}{\partial x}(\frac{xy)/z)	\frac{\partial\:}{\partial\:x}(\frac{xy}{z})
derivative of sqrt(7+xsec(x))	\frac{d}{dx}(\sqrt{7+x\sec(x)})
integral of xe^{-x}	\int\:xe^{-x}dx
derivative of 64e^{4x}	\frac{d}{dx}(64e^{4x})
derivative of ccost+t^2sin(t)	\frac{d}{dx}(ccost+t^{2}\sin(t))
area x^2+2x+11,-4x+2,0	area\:x^{2}+2x+11,-4x+2,0
derivative of f(x)=8xe^{9x}	derivative\:f(x)=8xe^{9x}
integral of (cos(x)+1/5 x)	\int\:(\cos(x)+\frac{1}{5}x)dx
integral of (x^3)/(1+x^4)	\int\:\frac{x^{3}}{1+x^{4}}dx
(\partial)/(\partial x)((e^x(y-x))dx)	\frac{\partial\:}{\partial\:x}((e^{x}(y-x))dx)
integral of x/(2x^2+4)	\int\:\frac{x}{2x^{2}+4}dx
integral of (csc^2(sqrt(x)))/(2sqrt(x))	\int\:\frac{\csc^{2}(\sqrt{x})}{2\sqrt{x}}dx
derivative of 2sin(x-2)	\frac{d}{dx}(2\sin(x-2))
derivative of 9-x^{2/3}	\frac{d}{dx}(9-x^{\frac{2}{3}})
(cos^3(x))^'	(\cos^{3}(x))^{\prime\:}
tangent of f(x)= 2/x ,\at x=-4	tangent\:f(x)=\frac{2}{x},\at\:x=-4
integral of (x^3)/(x^4-5)	\int\:\frac{x^{3}}{x^{4}-5}dx
integral of (x^2-18x+32)/(x(x-4)^2)	\int\:\frac{x^{2}-18x+32}{x(x-4)^{2}}dx
derivative of f(x)=x^{2/5}	derivative\:f(x)=x^{\frac{2}{5}}
laplacetransform 2sin(3t)+5cos(3t)	laplacetransform\:2\sin(3t)+5\cos(3t)
y^{''}+13y=0	y^{\prime\:\prime\:}+13y=0
(dy)/(dx)=(x+xy^2)/(4y)	\frac{dy}{dx}=\frac{x+xy^{2}}{4y}
integral from 0 to (3pi)/2 of cos^3(17x)	\int\:_{0}^{\frac{3π}{2}}\cos^{3}(17x)dx
area y=sqrt(x+1),x=8	area\:y=\sqrt{x+1},x=8
integral of x^2-2x+2	\int\:x^{2}-2x+2dx
derivative of f(x)=(1-cos(x))/(sin(x))	derivative\:f(x)=\frac{1-\cos(x)}{\sin(x)}
slope of f(x)=x^2+2x+1	slope\:f(x)=x^{2}+2x+1
integral of (1-x)(e-x+1)	\int\:(1-x)(e-x+1)dx
derivative of 1/(2x^2-2x+1)	\frac{d}{dx}(\frac{1}{2x^{2}-2x+1})
limit as x approaches infinity of pi5^x	\lim\:_{x\to\:\infty\:}(π5^{x})
area y=x^2-2x,y=-x^4	area\:y=x^{2}-2x,y=-x^{4}
derivative of y=7x^3+2	derivative\:y=7x^{3}+2
integral of (t+200)^2	\int\:(t+200)^{2}dt
derivative of (2-xe^x/(x+e^x))	\frac{d}{dx}(\frac{2-xe^{x}}{x+e^{x}})
y^{'''}-3y^{''}+3y^'-y=x-4e^x	y^{\prime\:\prime\:\prime\:}-3y^{\prime\:\prime\:}+3y^{\prime\:}-y=x-4e^{x}
integral of sin(2x-1)	\int\:\sin(2x-1)dx
x^2y^'-xy=y^2	x^{2}y^{\prime\:}-xy=y^{2}
(\partial)/(\partial y)(sqrt(y))	\frac{\partial\:}{\partial\:y}(\sqrt{y})
4/3 xy^'-3/8 y=0	\frac{4}{3}xy^{\prime\:}-\frac{3}{8}y=0
integral of 2xcos(3x)	\int\:2x\cos(3x)dx
derivative of 2xln(3x-4)	derivative\:2x\ln(3x-4)
slope of (-17,-13),(-9,7)	slope\:(-17,-13),(-9,7)
derivative of (ln(5x)/(sqrt(x)))	\frac{d}{dx}(\frac{\ln(5x)}{\sqrt{x}})
integral from 1 to 7 of 1/(36+(x-1)^2)	\int\:_{1}^{7}\frac{1}{36+(x-1)^{2}}dx
integral from-3 to 3 of 1	\int\:_{-3}^{3}1dx
laplacetransform sin(7t)	laplacetransform\:\sin(7t)
(\partial)/(\partial x)(10sqrt(x))	\frac{\partial\:}{\partial\:x}(10\sqrt{x})
integral from-1 to 2 of (3x^2-4x-1)	\int\:_{-1}^{2}(3x^{2}-4x-1)dx
d/(dt)(2t-t^2)	\frac{d}{dt}(2t-t^{2})
integral of sin(4x)cos(3x)	\int\:\sin(4x)\cos(3x)dx
integral of (x^2+6)e^{-x}	\int\:(x^{2}+6)e^{-x}dx
integral of 7/(sqrt(x))+7sqrt(x)	\int\:\frac{7}{\sqrt{x}}+7\sqrt{x}dx
(\partial ^2)/(\partial x^2)(ln(x+2y))	\frac{\partial\:^{2}}{\partial\:x^{2}}(\ln(x+2y))
sum from n=1 to infinity of 1/(3n^2+2)	\sum\:_{n=1}^{\infty\:}\frac{1}{3n^{2}+2}
derivative of (2cos(x-3)/(sin(x)))	\frac{d}{dx}(\frac{2\cos(x)-3}{\sin(x)})
limit as x approaches 0 of 1-(cos(5x))/x	\lim\:_{x\to\:0}(1-\frac{\cos(5x)}{x})
slope of (2.3)(4.3)	slope\:(2.3)(4.3)
derivative of-12xsin(x^2-8x^3cos(x^2))	\frac{d}{dx}(-12x\sin(x^{2})-8x^{3}\cos(x^{2}))
limit as x approaches pi of tan(x)	\lim\:_{x\to\:π}(\tan(x))
derivative of y=x^2e^x-2xe^x+7e^x	derivative\:y=x^{2}e^{x}-2xe^{x}+7e^{x}
x^2y^{''}+7xy^'+8y= 6/x	x^{2}y^{\prime\:\prime\:}+7xy^{\prime\:}+8y=\frac{6}{x}
derivative of f(x)=8x^4	derivative\:f(x)=8x^{4}
integral of ((6+6x))/(1+x^2)	\int\:\frac{(6+6x)}{1+x^{2}}dx
integral of x^2cos(x)+2sin(x)	\int\:x^{2}\cos(x)+2\sin(x)dx
integral from-infinity to 0 of xe^{7x}	\int\:_{-\infty\:}^{0}xe^{7x}dx
integral of 21e^{42x}arctan(e^{21x})	\int\:21e^{42x}\arctan(e^{21x})dx
derivative of y=(3x-14)^5	\frac{d}{dx}y=(3x-14)^{5}

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