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Popular Calculus Problems

integral of x^3(x^4-1)^2	\int\:x^{3}(x^{4}-1)^{2}dx
integral of 8cos(4x)	\int\:8\cos(4x)dx
derivative of (x^3/(x+1))	\frac{d}{dx}(\frac{x^{3}}{x+1})
limit as x approaches 0 of x^{3sin(x)}	\lim\:_{x\to\:0}(x^{3\sin(x)})
integral of (7x^3-2x^2+4)	\int\:(7x^{3}-2x^{2}+4)dx
integral of 9tan^2(x)	\int\:9\tan^{2}(x)dx
integral from-1 to 2 of 1/(x^4)	\int\:_{-1}^{2}\frac{1}{x^{4}}dx
y^{''}+2y^'+y=0,y(1)=1,y^'(1)=0	y^{\prime\:\prime\:}+2y^{\prime\:}+y=0,y(1)=1,y^{\prime\:}(1)=0
derivative of x^4-4x^3+3x^2-3	\frac{d}{dx}(x^{4}-4x^{3}+3x^{2}-3)
integral of (x^2-2x+5)e^{-x}	\int\:(x^{2}-2x+5)e^{-x}dx
limit as x approaches-2 of 7x^2+8	\lim\:_{x\to\:-2}(7x^{2}+8)
derivative of cos(-3x)	derivative\:\cos(-3x)
derivative of sin(t)-sin(t)cos(t)-5t	derivative\:\sin(t)-\sin(t)\cos(t)-5t
derivative of f(t)=-(50)/(t^3)+5/(t^2)	derivative\:f(t)=-\frac{50}{t^{3}}+\frac{5}{t^{2}}
integral of etan(x)	\int\:e\tan(x)dx
(d^2)/(dx^2)(cos^2(t))	\frac{d^{2}}{dx^{2}}(\cos^{2}(t))
integral of (sin(2x))/(cos^2(2x)+5)	\int\:\frac{\sin(2x)}{\cos^{2}(2x)+5}dx
limit as x approaches 1 of 4x	\lim\:_{x\to\:1}(4x)
integral of sec^2(t)	\int\:\sec^{2}(t)dt
limit as x approaches 0+of ((e^x))/(2^x)	\lim\:_{x\to\:0+}(\frac{(e^{x})}{2^{x}})
integral of cos(x)(4+5sin^2(x))	\int\:\cos(x)(4+5\sin^{2}(x))dx
d/(dθ)(sin(2θ))	\frac{d}{dθ}(\sin(2θ))
inverse oflaplace ((3s+1))/(s^2+4s)	inverselaplace\:\frac{(3s+1)}{s^{2}+4s}
integral of ((x^3-x^2+2x-6))/x	\int\:\frac{(x^{3}-x^{2}+2x-6)}{x}dx
tangent of-2x^2+4x-4,\at x=3	tangent\:-2x^{2}+4x-4,\at\:x=3
y^'-7y=0	y^{\prime\:}-7y=0
limit as x approaches 0+of csc(x)	\lim\:_{x\to\:0+}(\csc(x))
f(t)=e^t*cos(t)	f(t)=e^{t}\cdot\:\cos(t)
t^2y^'+ty=4	t^{2}y^{\prime\:}+ty=4
derivative of 5^x	derivative\:5^{x}
integral from 0 to b/M of (v^2M^2-b)	\int\:_{0}^{\frac{b}{M}}(v^{2}M^{2}-b)dv
integral of ((3x-5))/(sqrt(2x^2-6x+3))	\int\:\frac{(3x-5)}{\sqrt{2x^{2}-6x+3}}dx
xyy^'=sqrt(1-y^2)	xyy^{\prime\:}=\sqrt{1-y^{2}}
integral of r^2sqrt(16-r^2)	\int\:r^{2}\sqrt{16-r^{2}}dr
derivative of (x^2(x^2+5)^2)	\frac{d}{dx}((x^{2})(x^{2}+5)^{2})
derivative of 200x	\frac{d}{dx}(200x)
derivative of (x^{-1/2}+2x(7-x^{-1}))	\frac{d}{dx}((x^{-\frac{1}{2}}+2x)(7-x^{-1}))
derivative of f(x)=-4x+5	derivative\:f(x)=-4x+5
tangent of 1/(x-5)	tangent\:\frac{1}{x-5}
tangent of y= 1/(x-6),(5,-1)	tangent\:y=\frac{1}{x-6},(5,-1)
integral of x^{-5}+x^{1/2}	\int\:x^{-5}+x^{\frac{1}{2}}dx
derivative of (-x^2+25^2)	\frac{d}{dx}((-x^{2}+25)^{2})
integral of 7/(x^3-125)	\int\:\frac{7}{x^{3}-125}dx
(\partial)/(\partial y)(sin^2(x-3y))	\frac{\partial\:}{\partial\:y}(\sin^{2}(x-3y))
derivative of scos(x)	\frac{d}{dx}(s\cos(x))
sum from n=2 to infinity of 1/(n^4)	\sum\:_{n=2}^{\infty\:}\frac{1}{n^{4}}
derivative of f(x)=9e^x+4/(\sqrt[3]{x)}	derivative\:f(x)=9e^{x}+\frac{4}{\sqrt[3]{x}}
(\partial)/(\partial y)(arctan(9x-9y))	\frac{\partial\:}{\partial\:y}(\arctan(9x-9y))
integral of sin(x)cos(3x)	\int\:\sin(x)\cos(3x)dx
limit as x approaches 1 of x^{(1/(x-1))}	\lim\:_{x\to\:1}(x^{(\frac{1}{x-1})})
limit as x approaches x of 1/x	\lim\:_{x\to\:x}(\frac{1}{x})
limit as x approaches 0-of (3x-1)/(2x)	\lim\:_{x\to\:0-}(\frac{3x-1}{2x})
integral of x/(sqrt(ax^2+b))	\int\:\frac{x}{\sqrt{ax^{2}+b}}dx
integral of cot(23x)	\int\:\cot(23x)dx
limit as x approaches 3 of x^2-x+1	\lim\:_{x\to\:3}(x^{2}-x+1)
limit as x approaches 2-of (x+1)/(x-2)	\lim\:_{x\to\:2-}(\frac{x+1}{x-2})
integral of 9tsin^2(t)	\int\:9t\sin^{2}(t)dt
y^'=(6xsec(y/x)+y)/x	y^{\prime\:}=\frac{6x\sec(\frac{y}{x})+y}{x}
derivative of-(8x/(x^2+1))	\frac{d}{dx}(-\frac{8x}{x^{2}+1})
derivative of ln(4log_{4}(x)+pi^3)	\frac{d}{dx}(\ln(4)\log_{4}(x)+π^{3})
limit as x approaches 2 of 3.9+9.6	\lim\:_{x\to\:2}(3.9+9.6)
sum from n=0 to infinity of (10)/(2^n)	\sum\:_{n=0}^{\infty\:}\frac{10}{2^{n}}
derivative of x/(6x+5)	\frac{d}{dx}(\frac{x}{6x+5})
d/(dt)(sin(t)*cos(t))	\frac{d}{dt}(\sin(t)\cdot\:\cos(t))
x(d^2y)/(dx^2)+(2(dy)/(dx))=0	x\frac{d^{2}y}{dx^{2}}+(2\frac{dy}{dx})=0
y^'-4/x y=(y^3)/(x^3)	y^{\prime\:}-\frac{4}{x}y=\frac{y^{3}}{x^{3}}
integral from 1 to 2 of x^4(ln(x))^2	\int\:_{1}^{2}x^{4}(\ln(x))^{2}dx
derivative of-1/(4(x+1^{3/2)})	\frac{d}{dx}(-\frac{1}{4(x+1)^{\frac{3}{2}}})
integral from 1 to 2 of (3/x)	\int\:_{1}^{2}(\frac{3}{x})dx
derivative of (-5/x)	\frac{d}{dx}(\frac{-5}{x})
integral of 1/(x^{-2)}	\int\:\frac{1}{x^{-2}}dx
sum from n=6 to infinity of e^{7-6n}	\sum\:_{n=6}^{\infty\:}e^{7-6n}
(\partial)/(\partial x)((x-y)^2)	\frac{\partial\:}{\partial\:x}((x-y)^{2})
(\partial)/(\partial y)(-1/y sin(x/y))	\frac{\partial\:}{\partial\:y}(-\frac{1}{y}\sin(\frac{x}{y}))
(d^2)/(dx^2)(5/(6x^4))	\frac{d^{2}}{dx^{2}}(\frac{5}{6x^{4}})
derivative of (x-1sin(x))	\frac{d}{dx}((x-1)\sin(x))
(\partial)/(\partial x)(ln(e^x+e^y))	\frac{\partial\:}{\partial\:x}(\ln(e^{x}+e^{y}))
d/(dy)(1+ye^{xy})	\frac{d}{dy}(1+ye^{xy})
integral of xtan(pix)	\int\:x\tan(πx)dx
(\partial)/(\partial x)(sin(4x-2y))	\frac{\partial\:}{\partial\:x}(\sin(4x-2y))
derivative of (sqrt(x)/(e^x+1))	\frac{d}{dx}(\frac{\sqrt{x}}{e^{x}+1})
(\partial)/(\partial x)(xe^{-3xy})	\frac{\partial\:}{\partial\:x}(xe^{-3xy})
sum from n=1 to infinity of n/3	\sum\:_{n=1}^{\infty\:}\frac{n}{3}
derivative of (3x-4/(6x^2-1))	\frac{d}{dx}(\frac{3x-4}{6x^{2}-1})
derivative of f(x)=ln(sqrt(5x-7))	derivative\:f(x)=\ln(\sqrt{5x-7})
integral of (x^2+9)/(x^2+4)	\int\:\frac{x^{2}+9}{x^{2}+4}dx
integral of 1/(7y)	\int\:\frac{1}{7y}dy
(dy)/(dx)=1-y/x	\frac{dy}{dx}=1-\frac{y}{x}
derivative of (arctanh(sqrt(3x^2))^3)	\frac{d}{dx}((\arctanh(\sqrt{3x^{2}}))^{3})
integral of xsin(z)	\int\:x\sin(z)dy
tangent of f(x)=(x^3-16x)^8,\at x=4	tangent\:f(x)=(x^{3}-16x)^{8},\at\:x=4
integral from 0 to infinity of e^{-bx}	\int\:_{0}^{\infty\:}e^{-bx}dx
sum from n=0 to infinity of (3/4)^n	\sum\:_{n=0}^{\infty\:}(\frac{3}{4})^{n}
taylor x^4+x	taylor\:x^{4}+x
integral of e^{4-x^2}	\int\:e^{4-x^{2}}dx
integral of (sin(x))/(cos^3(x)+cos(x))	\int\:\frac{\sin(x)}{\cos^{3}(x)+\cos(x)}dx
(d^3)/(dx^3)(sqrt(x))	\frac{d^{3}}{dx^{3}}(\sqrt{x})
maclaurin e^{4x}	maclaurin\:e^{4x}
integral of (cos(ln(4x^2)))/x	\int\:\frac{\cos(\ln(4x^{2}))}{x}dx
6y^'=y^2,y(0)=5	6y^{\prime\:}=y^{2},y(0)=5

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