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Popular Calculus Problems

derivative of sin(xcos^2(x))	\frac{d}{dx}(\sin(x)\cos^{2}(x))
integral of 1/(4-4sin(x))	\int\:\frac{1}{4-4\sin(x)}dx
integral of 8x^7e^{7x^8}	\int\:8x^{7}e^{7x^{8}}dx
integral of (-6x^3+8x^2-30x+10)/(x^3+5x)	\int\:\frac{-6x^{3}+8x^{2}-30x+10}{x^{3}+5x}dx
integral of x^2+6	\int\:x^{2}+6dx
derivative of xsqrt(ln(x))	derivative\:x\sqrt{\ln(x)}
integral of (e^{-x})/(e^{-x)+1}	\int\:\frac{e^{-x}}{e^{-x}+1}dx
derivative of 6e^{-2x}cos(4x)	derivative\:6e^{-2x}\cos(4x)
derivative of f(x)=5x^2-2x-7	derivative\:f(x)=5x^{2}-2x-7
y^'=0.04y-2000,y(0)=25000	y^{\prime\:}=0.04y-2000,y(0)=25000
laplacetransform e^{3(t-2)}	laplacetransform\:e^{3(t-2)}
derivative of (2x/(3+x^2))	\frac{d}{dx}(\frac{2x}{3+x^{2}})
integral of x*sqrt(1-x^2)	\int\:x\cdot\:\sqrt{1-x^{2}}dx
derivative of f(x)=2x^2-3x+6	derivative\:f(x)=2x^{2}-3x+6
derivative of f(x)=log_{2}(x^2+1)-2^3	derivative\:f(x)=\log_{2}(x^{2}+1)-2^{3}
(\partial)/(\partial x)(y+3)	\frac{\partial\:}{\partial\:x}(y+3)
integral of p(p+6)^8	\int\:p(p+6)^{8}dp
derivative of (0.2x/(x^2+9))	\frac{d}{dx}(\frac{0.2x}{x^{2}+9})
integral of 1-x^9	\int\:1-x^{9}dx
(\partial)/(\partial x)(-1/x)	\frac{\partial\:}{\partial\:x}(-\frac{1}{x})
integral of e^xcos(3x)	\int\:e^{x}\cos(3x)dx
sum from n=1 to infinity of 5^nx^nn!	\sum\:_{n=1}^{\infty\:}5^{n}x^{n}n!
derivative of 7e^{2x^4-3x}	\frac{d}{dx}(7e^{2x^{4}-3x})
integral of 4t^5	\int\:4t^{5}dt
inverse oflaplace 8/((9s^2+9s+4)(s))	inverselaplace\:\frac{8}{(9s^{2}+9s+4)(s)}
(\partial)/(\partial x)(sqrt(x))	\frac{\partial\:}{\partial\:x}(\sqrt{x})
derivative of ((t-4)^3)/6+t^2	derivative\:\frac{(t-4)^{3}}{6}+t^{2}
limit as x approaches 0 of 9sin(x)ln(x)	\lim\:_{x\to\:0}(9\sin(x)\ln(x))
integral of xln(y)	\int\:x\ln(y)dy
limit as x approaches 1/2 of x/(2x-1)	\lim\:_{x\to\:\frac{1}{2}}(\frac{x}{2x-1})
f(x)=(x^3+3x)(2x+4)	f(x)=(x^{3}+3x)(2x+4)
integral of (e^x)*cos(nx)	\int\:(e^{x})\cdot\:\cos(nx)dx
integral of xsqrt(x-10)	\int\:x\sqrt{x-10}dx
inverse oflaplace 3/s+(16)/(s(s+1))	inverselaplace\:\frac{3}{s}+\frac{16}{s(s+1)}
integral from 1 to e^2 of (ln(x))/(x^2)	\int\:_{1}^{e^{2}}\frac{\ln(x)}{x^{2}}dx
(\partial)/(\partial x)((a-b^2)/(x-c^2))	\frac{\partial\:}{\partial\:x}(\frac{a-b^{2}}{x-c^{2}})
derivative of 5-4/x	\frac{d}{dx}(5-\frac{4}{x})
derivative of (-u^2+7)/((u^2+7)^2)	derivative\:\frac{-u^{2}+7}{(u^{2}+7)^{2}}
derivative of sec(x^5+x)	\frac{d}{dx}(\sec(x^{5}+x))
slope ofintercept (1.1)(0.5)	slopeintercept\:(1.1)(0.5)
integral of sqrt(1+5x^2)(10x)	\int\:\sqrt{1+5x^{2}}(10x)dx
derivative of y=3x^2+(10x)/3-2	derivative\:y=3x^{2}+\frac{10x}{3}-2
derivative of (tan^3(x)/3)	\frac{d}{dx}(\frac{\tan^{3}(x)}{3})
sum from n=1 to infinity of (2n!)/(n^5)	\sum\:_{n=1}^{\infty\:}\frac{2n!}{n^{5}}
(\partial)/(\partial x)(-6e^{-3x^2-y^2}x)	\frac{\partial\:}{\partial\:x}(-6e^{-3x^{2}-y^{2}}x)
slope of (1-2x)(3x-4),\at x=2	slope\:(1-2x)(3x-4),\at\:x=2
f(x)=sqrt(2x^2-x+9)	f(x)=\sqrt{2x^{2}-x+9}
derivative of f(x)=2-2/3 x	derivative\:f(x)=2-\frac{2}{3}x
derivative of ln(ln(sec(2x)))	\frac{d}{dx}(\ln(\ln(\sec(2x))))
derivative of y=3x+4/x	derivative\:y=3x+\frac{4}{x}
(du+2dv)/(u+2v)=0	\frac{du+2dv}{u+2v}=0
limit as x approaches 2 of 3x^2-2x+1	\lim\:_{x\to\:2}(3x^{2}-2x+1)
derivative of f(x)=(7x^2+7x+7)/(sqrt(x))	derivative\:f(x)=\frac{7x^{2}+7x+7}{\sqrt{x}}
tangent of y=(x^{(3)}-4x)^{(12)}(2)	tangent\:y=(x^{(3)}-4x)^{(12)}(2)
(\partial)/(\partial y)(sqrt(y+cos^2(x)))	\frac{\partial\:}{\partial\:y}(\sqrt{y+\cos^{2}(x)})
integral of 1/(sqrt(x^2-6x))	\int\:\frac{1}{\sqrt{x^{2}-6x}}dx
sum from n=1 to infinity of tan(3n)	\sum\:_{n=1}^{\infty\:}\tan(3n)
derivative of g(x)=(x^2-64)/(x+8)	derivative\:g(x)=\frac{x^{2}-64}{x+8}
y^{''}+6y^'+5y=-3te^{(4t)}	y^{\prime\:\prime\:}+6y^{\prime\:}+5y=-3te^{(4t)}
integral of 2sqrt(x)-\sqrt[3]{x}-x^4	\int\:2\sqrt{x}-\sqrt[3]{x}-x^{4}dx
(\partial)/(\partial x)(-x/(x^2+y^2))	\frac{\partial\:}{\partial\:x}(-\frac{x}{x^{2}+y^{2}})
integral of 5cos(x)-4sin(x)	\int\:5\cos(x)-4\sin(x)dx
derivative of y=\sqrt[4]{(cos(x))^3}	derivative\:y=\sqrt[4]{(\cos(x))^{3}}
derivative of (2x+3^2)	\frac{d}{dx}((2x+3)^{2})
derivative of f(x)=a^4+cos^4(x)	derivative\:f(x)=a^{4}+\cos^{4}(x)
integral from 0 to 1 of 2pi(2-y)(4y^2)	\int\:_{0}^{1}2π(2-y)(4y^{2})dy
integral of-sin(x	\int\:-\sin(d)xdx
integral from 0 to 1 of \sqrt[4]{x}	\int\:_{0}^{1}\sqrt[4]{x}dx
integral of (x+1)e^{3x^2+6x}	\int\:(x+1)e^{3x^{2}+6x}dx
derivative of Axe^{-2x}	\frac{d}{dx}(Axe^{-2x})
derivative of (2x-x^2/(3x^2+2))	\frac{d}{dx}(\frac{2x-x^{2}}{3x^{2}+2})
(\partial)/(\partial x)(x/(x^7-y^4))	\frac{\partial\:}{\partial\:x}(\frac{x}{x^{7}-y^{4}})
derivative of (7x^2/(x^3))	\frac{d}{dx}(\frac{7x^{2}}{x^{3}})
limit as x approaches 0 of (1+x)^{7/x}	\lim\:_{x\to\:0}((1+x)^{\frac{7}{x}})
k((dx)/(dt))=x+15	k(\frac{dx}{dt})=x+15
integral from 0 to 10 of x	\int\:_{0}^{10}xdx
derivative of ((x^2+1^2)/((x^4+1)^4))	\frac{d}{dx}(\frac{(x^{2}+1)^{2}}{(x^{4}+1)^{4}})
limit as x approaches 2 of (2x-8)/(x-1)	\lim\:_{x\to\:2}(\frac{2x-8}{x-1})
derivative of 4tsin(pit)	derivative\:4t\sin(πt)
x^3y^{'''}+3x^2y^{''}-2xy^'+2y=0	x^{3}y^{\prime\:\prime\:\prime\:}+3x^{2}y^{\prime\:\prime\:}-2xy^{\prime\:}+2y=0
limit as x approaches 5 of 6/(x-5)	\lim\:_{x\to\:5}(\frac{6}{x-5})
integral of (sin(x))/((cos(x))^3)	\int\:\frac{\sin(x)}{(\cos(x))^{3}}dx
(\partial)/(\partial x)((x^4+y^2)/(xy))	\frac{\partial\:}{\partial\:x}(\frac{x^{4}+y^{2}}{xy})
integral of sqrt(9x+5)	\int\:\sqrt{9x+5}dx
limit as x approaches-6+of (-2x)/(x+6)	\lim\:_{x\to\:-6+}(\frac{-2x}{x+6})
slope ofintercept (0.2)(2)	slopeintercept\:(0.2)(2)
derivative of x^{10}e^{x+1}	\frac{d}{dx}(x^{10}e^{x+1})
(dy)/(dt)=y(1-y),y(0)=16	\frac{dy}{dt}=y(1-y),y(0)=16
integral of (t^2-1)/(t^4-1)	\int\:\frac{t^{2}-1}{t^{4}-1}dt
y^{''}+4y^'+4y=e^{-2x}*ln(x)	y^{\prime\:\prime\:}+4y^{\prime\:}+4y=e^{-2x}\cdot\:\ln(x)
derivative of (sin(x)/(bsin(bx)))	\frac{d}{dx}(\frac{\sin(x)}{b\sin(bx)})
y^'-2xy=2xe^{x^2}	y^{\prime\:}-2xy=2xe^{x^{2}}
((4x^2+5)^2*(7x)^{2x})^'	((4x^{2}+5)^{2}\cdot\:(7x)^{2x})^{\prime\:}
-4x^2y+y^'=4x^2	-4x^{2}y+y^{\prime\:}=4x^{2}
integral of 1/(12sqrt(x)+12x)	\int\:\frac{1}{12\sqrt{x}+12x}dx
integral of x*(7-x)^9	\int\:x\cdot\:(7-x)^{9}dx
derivative of 1/(4(1+x^{3/4)})	\frac{d}{dx}(\frac{1}{4(1+x)^{\frac{3}{4}}})
integral of (sin(x))/(cos^5(x))	\int\:\frac{\sin(x)}{\cos^{5}(x)}dx
derivative of 5x^2-1	\frac{d}{dx}(5x^{2}-1)
(dN)/(dt)+N=Nte^{(t+2)}	\frac{dN}{dt}+N=Nte^{(t+2)}

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