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Popular Calculus Problems

integral from 0 to 21 of xsqrt(21-x)	\int\:_{0}^{21}x\sqrt{21-x}dx
integral of (e^x-5)^2	\int\:(e^{x}-5)^{2}dx
(\partial)/(\partial x)(xy+z^2)	\frac{\partial\:}{\partial\:x}(xy+z^{2})
integral of (y+1)/(y+3)	\int\:\frac{y+1}{y+3}dy
integral of (11x-7)^{-3}	\int\:(11x-7)^{-3}dx
integral of sin(6x)cos(9x)	\int\:\sin(6x)\cos(9x)dx
(\partial)/(\partial x)(3y^6cos(3x))	\frac{\partial\:}{\partial\:x}(3y^{6}\cos(3x))
integral from 0 to 9 of sqrt(162-x^2)	\int\:_{0}^{9}\sqrt{162-x^{2}}dx
(\partial)/(\partial x)(2e^{xy^2})	\frac{\partial\:}{\partial\:x}(2e^{xy^{2}})
integral of ((3x-1))/(xsqrt(x^2-4))	\int\:\frac{(3x-1)}{x\sqrt{x^{2}-4}}dx
y^{''}-y=8xe^x	y^{\prime\:\prime\:}-y=8xe^{x}
limit as x approaches 1 of 7^{x^4-x^2}	\lim\:_{x\to\:1}(7^{x^{4}-x^{2}})
integral from 0 to 1 of ln(x+1)	\int\:_{0}^{1}\ln(x+1)dx
derivative of y=((4x^2+6x+8))/(sqrt(x))	derivative\:y=\frac{(4x^{2}+6x+8)}{\sqrt{x}}
derivative of-4e^{-x/3}-2	derivative\:-4e^{-\frac{x}{3}}-2
tangent of f(x)=-9/2 x^2+7x+7,\at x=-1	tangent\:f(x)=-\frac{9}{2}x^{2}+7x+7,\at\:x=-1
area sqrt(16-x),12,16	area\:\sqrt{16-x},12,16
derivative of (3+4x-x^2^{1/2})	\frac{d}{dx}((3+4x-x^{2})^{\frac{1}{2}})
y^{''}+4y=2t^2	y^{\prime\:\prime\:}+4y=2t^{2}
tangent of f(x)=4x^2-2x+3	tangent\:f(x)=4x^{2}-2x+3
derivative of log_{e}(tan(x))	\frac{d}{dx}(\log_{e}(\tan(x)))
derivative of (x^2-8x/(2x-3))	\frac{d}{dx}(\frac{x^{2}-8x}{2x-3})
integral of-1/(2sqrt(x))	\int\:-\frac{1}{2\sqrt{x}}dx
tangent of (6x)/(sqrt(4-x^2)),\at x=0	tangent\:\frac{6x}{\sqrt{4-x^{2}}},\at\:x=0
derivative of 4sqrt(7x^2+9)	\frac{d}{dx}(4\sqrt{7x^{2}+9})
integral of x/(x^2+4)	\int\:\frac{x}{x^{2}+4}dx
derivative of 5sqrt(x)(x^3-5sqrt(x)+5)	derivative\:5\sqrt{x}(x^{3}-5\sqrt{x}+5)
(\partial)/(\partial x)(4ln((2xy)/(7z)))	\frac{\partial\:}{\partial\:x}(4\ln(\frac{2xy}{7z}))
derivative of h(w)=(4w^5-w)/w	derivative\:h(w)=\frac{4w^{5}-w}{w}
integral of xe^{1-x}	\int\:xe^{1-x}dx
f(x)=xsin(1/x)	f(x)=x\sin(\frac{1}{x})
tangent of y=x^2-3x-2,(2,-4)	tangent\:y=x^{2}-3x-2,(2,-4)
area x=2-y^2,x=y^4	area\:x=2-y^{2},x=y^{4}
limit as x approaches 3-of 4/(x^2-9)	\lim\:_{x\to\:3-}(\frac{4}{x^{2}-9})
area x^2,2-x	area\:x^{2},2-x
integral of (e^{4x})/(4x)	\int\:\frac{e^{4x}}{4x}dx
(dy)/(dt)=3-2y	\frac{dy}{dt}=3-2y
derivative of ln(2+sin(x))	\frac{d}{dx}(\ln(2+\sin(x)))
derivative of (2x^2)/(3y^2)	derivative\:\frac{2x^{2}}{3y^{2}}
y^'+y/x =4x^2	y^{\prime\:}+\frac{y}{x}=4x^{2}
(dy)/(dx)=(e^x)/(5+e^x)	\frac{dy}{dx}=\frac{e^{x}}{5+e^{x}}
integral of ((ln(z))^3)/z	\int\:\frac{(\ln(z))^{3}}{z}dz
limit as x approaches 0 of 1/(4x)-1/((e^{4x)-1)}	\lim\:_{x\to\:0}(\frac{1}{4x}-\frac{1}{(e^{4x}-1)})
integral of 1/(x^{11/5)}	\int\:\frac{1}{x^{\frac{11}{5}}}dx
(\partial)/(\partial x)(tan(9+2x^2y^3z^2))	\frac{\partial\:}{\partial\:x}(\tan(9+2x^{2}y^{3}z^{2}))
(\partial)/(\partial x)(ln(z))	\frac{\partial\:}{\partial\:x}(\ln(z))
limit as x approaches 0 of 1-(tan(kx))/x	\lim\:_{x\to\:0}(1-\frac{\tan(kx)}{x})
derivative of 1/((1-x^3))	\frac{d}{dx}(\frac{1}{(1-x)^{3}})
derivative of ((ln(x)^2)/x)	\frac{d}{dx}(\frac{(\ln(x))^{2}}{x})
xy^'+2y=6x^2sqrt(y)	xy^{\prime\:}+2y=6x^{2}\sqrt{y}
integral of (x')/(sqrt(x))	\int\:\frac{x\prime\:}{\sqrt{x}}dx
limit as x approaches-infinity of-4	\lim\:_{x\to\:-\infty\:}(-4)
integral of e^u	\int\:e^{u}du
inverse oflaplace (100)/(s^3(s-2))	inverselaplace\:\frac{100}{s^{3}(s-2)}
limit as x approaches-5 of 217	\lim\:_{x\to\:-5}(217)
sum from n=1 to infinity of 3^n 1/(n!)	\sum\:_{n=1}^{\infty\:}3^{n}\frac{1}{n!}
derivative of e^{-4x}cos(4x)	\frac{d}{dx}(e^{-4x}\cos(4x))
(\partial)/(\partial x)(3x^4)	\frac{\partial\:}{\partial\:x}(3x^{4})
derivative of y=6x^2-x^3	derivative\:y=6x^{2}-x^{3}
(dy)/(dx)=sqrt(x+y)-1	\frac{dy}{dx}=\sqrt{x+y}-1
integral of (7cos(sqrt(x)))	\int\:(7\cos(\sqrt{x}))dx
limit as x approaches 0 of ((x+2)^3-8)/x	\lim\:_{x\to\:0}(\frac{(x+2)^{3}-8}{x})
(\partial)/(\partial x)(ln(1+x^2+y^2+z^2))	\frac{\partial\:}{\partial\:x}(\ln(1+x^{2}+y^{2}+z^{2}))
derivative of f(x)=(1+2x^2)(x-x^2)	derivative\:f(x)=(1+2x^{2})(x-x^{2})
integral from 0 to 5 of 2pi(6-x)(25-x^2)	\int\:_{0}^{5}2π(6-x)(25-x^{2})dx
derivative of arcsin(cos(x^6))	derivative\:\arcsin(\cos(x^{6}))
derivative of log_{2x+1}(2x+3)	\frac{d}{dx}(\log_{2x+1}(2x+3))
limit as h approaches 0 of (6xh+3h^2)/h	\lim\:_{h\to\:0}(\frac{6xh+3h^{2}}{h})
(\partial)/(\partial x)(3e^{x^3y^3})	\frac{\partial\:}{\partial\:x}(3e^{x^{3}y^{3}})
integral of 7xsin^2(x)	\int\:7x\sin^{2}(x)dx
tangent of sqrt(7x+4)	tangent\:\sqrt{7x+4}
derivative of 5sec(6x)	derivative\:5\sec(6x)
integral from 0 to ln(15) of xe^x	\int\:_{0}^{\ln(15)}xe^{x}dx
integral of 2x(x^2+2)^4	\int\:2x(x^{2}+2)^{4}dx
derivative of-3sin(x/3)	\frac{d}{dx}(-3\sin(\frac{x}{3}))
integral of e^{3x+9}	\int\:e^{3x+9}dx
laplacetransform 7sin(4t+8)+3cos(4t-2)	laplacetransform\:7\sin(4t+8)+3\cos(4t-2)
limit as x approaches 1 of 1-x-[x]	\lim\:_{x\to\:1}(1-x-[x])
integral of (1+x^2)	\int\:(1+x^{2})dx
derivative of (2x-3/(x^2-1))	\frac{d}{dx}(\frac{2x-3}{x^{2}-1})
derivative of 2xsin(x^2)-cos(x)-e^{-x-2}	derivative\:2x\sin(x^{2})-\cos(x)-e^{-x-2}
integral of (6x+y)	\int\:(6x+y)dx
xy'+(1+xcot(x))y=0	xy\prime\:+(1+x\cot(x))y=0
integral from-5 to 0 of 1/(sqrt(4-x))	\int\:_{-5}^{0}\frac{1}{\sqrt{4-x}}dx
integral of (1/(x^2)-4/(x^3))	\int\:(\frac{1}{x^{2}}-\frac{4}{x^{3}})dx
(\partial)/(\partial x)(3xz+y^2)	\frac{\partial\:}{\partial\:x}(3xz+y^{2})
integral from 1 to 16 of 1/(9-sqrt(x))	\int\:_{1}^{16}\frac{1}{9-\sqrt{x}}dx
tangent of f(x)=tan(3x),\at x= pi/9	tangent\:f(x)=\tan(3x),\at\:x=\frac{π}{9}
integral of sqrt(2+2cos(4x))	\int\:\sqrt{2+2\cos(4x)}dx
(\partial)/(\partial y)(x/((x^2+y^2)))	\frac{\partial\:}{\partial\:y}(\frac{x}{(x^{2}+y^{2})})
derivative of sin((2x/(x^4-4x)))	\frac{d}{dx}(\sin(\frac{2x}{x^{4}-4x}))
sum from n=0 to infinity of 9/(n(n+3))	\sum\:_{n=0}^{\infty\:}\frac{9}{n(n+3)}
integral of (x^2)	\int\:(x^{2})dx
derivative of (2x^{2x})	\frac{d}{dx}((2x)^{2x})
derivative of 4x^3sec(7x)	\frac{d}{dx}(4x^{3}\sec(7x))
(x^2+1)y^'+7x(y-1)=0	(x^{2}+1)y^{\prime\:}+7x(y-1)=0
(x-2)y^'-y=2(x-2)^3,y(3)=5	(x-2)y^{\prime\:}-y=2(x-2)^{3},y(3)=5
integral of (2xln(x^2+1))/(x^2+1)	\int\:\frac{2x\ln(x^{2}+1)}{x^{2}+1}dx
tangent of sqrt(x^2+16),\at x=3	tangent\:\sqrt{x^{2}+16},\at\:x=3
integral of 1/3 x^3sqrt(9-x^2)	\int\:\frac{1}{3}x^{3}\sqrt{9-x^{2}}dx

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