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Popular Calculus Problems

integral of (x-3)sin(pix)	\int\:(x-3)\sin(πx)dx
integral of (cot(sqrt(x)))/(sqrt(x))	\int\:\frac{\cot(\sqrt{x})}{\sqrt{x}}dx
(\partial)/(\partial x)(ln(x+4y+7z))	\frac{\partial\:}{\partial\:x}(\ln(x+4y+7z))
derivative of (x-1^2+1)	\frac{d}{dx}((x-1)^{2}+1)
(\partial)/(\partial x)(cos(ye^{x*y}))	\frac{\partial\:}{\partial\:x}(\cos(ye^{x\cdot\:y}))
integral of [1+1/((x+1)^2)]	\int\:[1+\frac{1}{(x+1)^{2}}]dx
limit as x approaches 2 of 4-x	\lim\:_{x\to\:2}(4-x)
derivative of y=(x^5)/(3-x^4)	derivative\:y=\frac{x^{5}}{3-x^{4}}
(\partial)/(\partial y)(ln(2x^2+y^2))	\frac{\partial\:}{\partial\:y}(\ln(2x^{2}+y^{2}))
limit as x approaches 4 of (x-4)/(x^2+3x-28)	\lim\:_{x\to\:4}(\frac{x-4}{x^{2}+3x-28})
limit as x approaches infinity of x/(12)	\lim\:_{x\to\:\infty\:}(\frac{x}{12})
derivative of (sqrt(x)-7/(sqrt(x)+5))	\frac{d}{dx}(\frac{\sqrt{x}-7}{\sqrt{x}+5})
derivative of (0.3(9^x)/(x^3))	\frac{d}{dx}(\frac{0.3(9^{x})}{x^{3}})
(\partial)/(\partial x)(x^2yz-xyz^5)	\frac{\partial\:}{\partial\:x}(x^{2}yz-xyz^{5})
y^{'''}-y^{''}+7y^'-7y=0	y^{\prime\:\prime\:\prime\:}-y^{\prime\:\prime\:}+7y^{\prime\:}-7y=0
limit as x approaches 0 of x^3x	\lim\:_{x\to\:0}(x^{3}x)
integral from 0 to 5 of (x+y)/(55)	\int\:_{0}^{5}\frac{x+y}{55}dx
(\partial)/(\partial x)(4arctan(y/x))	\frac{\partial\:}{\partial\:x}(4\arctan(\frac{y}{x}))
derivative of sin(e^x(x^2-x))	\frac{d}{dx}(\sin(e^{x}(x^{2}-x)))
tangent of 2x^2-2x-4,\at x=1	tangent\:2x^{2}-2x-4,\at\:x=1
derivative of (cos(x))/(x^5)	derivative\:\frac{\cos(x)}{x^{5}}
derivative of x/(6-x)	\frac{d}{dx}(\frac{x}{6-x})
derivative of y=3x^2+12x+6	derivative\:y=3x^{2}+12x+6
limit as x approaches 2 of 8-3x+12x^2	\lim\:_{x\to\:2}(8-3x+12x^{2})
derivative of (56/(x^9))	\frac{d}{dx}(\frac{56}{x^{9}})
integral from 0 to 3 of 1/x	\int\:_{0}^{3}\frac{1}{x}dx
derivative of (27/((x+5)^{4/3)})	\frac{d}{dx}(\frac{27}{(x+5)^{\frac{4}{3}}})
integral of sin(t)*sin(t)	\int\:\sin(t)\cdot\:\sin(t)dt
limit as n approaches infinity of 7n^{5/4}	\lim\:_{n\to\:\infty\:}(7n^{\frac{5}{4}})
y^'-y=9te^2t,y(0)=1	y^{\prime\:}-y=9te^{2}t,y(0)=1
integral of-(1-cos^2(x))/(cos(x))	\int\:-\frac{1-\cos^{2}(x)}{\cos(x)}dx
integral from 0 to pi/4 of cos^4(x)	\int\:_{0}^{\frac{π}{4}}\cos^{4}(x)dx
derivative of 25x^4+30x^3-11x^2-12x+4	derivative\:25x^{4}+30x^{3}-11x^{2}-12x+4
(5t+3y+6)dt-dy=0	(5t+3y+6)dt-dy=0
y^'-3y=9x	y^{\prime\:}-3y=9x
slope of (-3,-1),(8,2)	slope\:(-3,-1),(8,2)
(\partial)/(\partial x)(x^4-x^3y+xy^3-y^4)	\frac{\partial\:}{\partial\:x}(x^{4}-x^{3}y+xy^{3}-y^{4})
limit as x approaches 0 of 1/x+1/(\|x\|)	\lim\:_{x\to\:0}(\frac{1}{x}+\frac{1}{\left\|x\right\|})
derivative of y=(x^6)/6+1/(16x^4)	derivative\:y=\frac{x^{6}}{6}+\frac{1}{16x^{4}}
integral from-1 to 1 of (x^2)/(1+x^6)	\int\:_{-1}^{1}\frac{x^{2}}{1+x^{6}}dx
derivative of (cos(x))/(e^x)	derivative\:\frac{\cos(x)}{e^{x}}
integral of (7x^2-4x)e^{2x}	\int\:(7x^{2}-4x)e^{2x}dx
limit as x approaches 1 of ((x^5-1))/(x^3-1)	\lim\:_{x\to\:1}(\frac{(x^{5}-1)}{x^{3}-1})
tangent of-0.025x^2+4x	tangent\:-0.025x^{2}+4x
(\partial)/(\partial x)(y^2sin(xy))	\frac{\partial\:}{\partial\:x}(y^{2}\sin(xy))
integral of (5^{3x}+cosh(x))	\int\:(5^{3x}+\cosh(x))dx
limit as x approaches 3 of 2^x	\lim\:_{x\to\:3}(2^{x})
integral of tan^5(x)sec^9(x)	\int\:\tan^{5}(x)\sec^{9}(x)dx
integral of (8x^2+9x+8)/((x^2+1)^2)	\int\:\frac{8x^{2}+9x+8}{(x^{2}+1)^{2}}dx
sum from n=0 to infinity of (3/7)^n	\sum\:_{n=0}^{\infty\:}(\frac{3}{7})^{n}
(dy)/(dx)=9x^3	\frac{dy}{dx}=9x^{3}
derivative of cot(pix*sec(pi)x)	\frac{d}{dx}(\cot(π)x\cdot\:\sec(π)x)
derivative of 5x+6	derivative\:5x+6
derivative of f(x)=ln(x+sqrt(x^2-12))	derivative\:f(x)=\ln(x+\sqrt{x^{2}-12})
tangent of y=(-2x)/((x^2+1))	tangent\:y=\frac{-2x}{(x^{2}+1)}
limit as x approaches 0 of x/0	\lim\:_{x\to\:0}(\frac{x}{0})
limit as x approaches-2 of x^2+3x-7	\lim\:_{x\to\:-2}(x^{2}+3x-7)
(\partial)/(\partial x)(-xyz^2+1)	\frac{\partial\:}{\partial\:x}(-xyz^{2}+1)
f(x)=-e^xx+3e^x	f(x)=-e^{x}x+3e^{x}
integral of (-1)/4 e^{-4x}3x^2	\int\:\frac{-1}{4}e^{-4x}3x^{2}dx
integral of 15(x+2)^4	\int\:15(x+2)^{4}dx
y^'=y(1-y),y(0)=-5	y^{\prime\:}=y(1-y),y(0)=-5
sum from n=0 to infinity of 1/((1+n)^2)	\sum\:_{n=0}^{\infty\:}\frac{1}{(1+n)^{2}}
derivative of 3cos(3x)	\frac{d}{dx}(3\cos(3x))
derivative of 4x^{5/4}+10x^{3/2}+5x	derivative\:4x^{\frac{5}{4}}+10x^{\frac{3}{2}}+5x
slope of (1,-2),(3,1)	slope\:(1,-2),(3,1)
y^{''}+36y=-60sin(6t)	y^{\prime\:\prime\:}+36y=-60\sin(6t)
(dy)/(dt)=-2(1+y^2)tan(2t)	\frac{dy}{dt}=-2(1+y^{2})\tan(2t)
derivative of ((sqrt(x)-7)/(sqrt(x)+7))	\frac{d}{dx}(\frac{(\sqrt{x}-7)}{\sqrt{x}+7})
integral of e^{2x}sin(3x)	\int\:e^{2x}\sin(3x)dx
integral from 1 to 12 of 1/(x-9)	\int\:_{1}^{12}\frac{1}{x-9}dx
sum from n=1 to infinity of 1/(n+4)	\sum\:_{n=1}^{\infty\:}\frac{1}{n+4}
(\partial)/(\partial x)(x*e^x+ln(x)y)	\frac{\partial\:}{\partial\:x}(x\cdot\:e^{x}+\ln(x)y)
integral of-7ln(x^2-1)	\int\:-7\ln(x^{2}-1)dx
sum from n=2 to infinity of 1/(n(n-1))	\sum\:_{n=2}^{\infty\:}\frac{1}{n(n-1)}
implicit (dy)/(dx),4y^2-5y+8=2x^2-3x	implicit\:\frac{dy}{dx},4y^{2}-5y+8=2x^{2}-3x
integral of 2x(1+x^2)^2	\int\:2x(1+x^{2})^{2}dx
y^{''}-4y^'+4y=2e^{2x}	y^{\prime\:\prime\:}-4y^{\prime\:}+4y=2e^{2x}
derivative of 5e^{-x}+e^{3x}	\frac{d}{dx}(5e^{-x}+e^{3x})
derivative of ln(x/(1+x^2))	\frac{d}{dx}(\ln(\frac{x}{1+x^{2}}))
integral of (2x)/((1+x^2)^2)	\int\:\frac{2x}{(1+x^{2})^{2}}dx
area y=14x,y=x^2	area\:y=14x,y=x^{2}
derivative of 4x^{2/3}	derivative\:4x^{\frac{2}{3}}
integral of 6cos^5(x)sin^4(x)	\int\:6\cos^{5}(x)\sin^{4}(x)dx
area x^{1/2},x=9	area\:x^{\frac{1}{2}},x=9
(\partial)/(\partial x)(bxe^{2xy})	\frac{\partial\:}{\partial\:x}(bxe^{2xy})
integral of sqrt(4x^2+9x^4)	\int\:\sqrt{4x^{2}+9x^{4}}dx
derivative of 10^{nx}	\frac{d}{dx}(10^{nx})
derivative of f(x)=(14)/((x+4)^3)	derivative\:f(x)=\frac{14}{(x+4)^{3}}
(dy}{dx}=\frac{cos(x))/y	\frac{dy}{dx}=\frac{\cos(x)}{y}
sum from n=1 to infinity of (5n)/(2n-1)	\sum\:_{n=1}^{\infty\:}\frac{5n}{2n-1}
integral of tk	\int\:tkdt
integral from 0 to 1 of x-1	\int\:_{0}^{1}x-1dx
derivative of 8/(sqrt(x))	derivative\:\frac{8}{\sqrt{x}}
integral of (x^5+4)^{12}x^4	\int\:(x^{5}+4)^{12}x^{4}dx
integral of (x^2+1)/((x-2)^3)	\int\:\frac{x^{2}+1}{(x-2)^{3}}dx
integral of (x+2)/(x^2)	\int\:\frac{x+2}{x^{2}}dx
area 2^x,-4,4	area\:2^{x},-4,4
integral of (3^x)/(3-3^x)	\int\:\frac{3^{x}}{3-3^{x}}dx
derivative of (ln(x)/(sin(x)))	\frac{d}{dx}(\frac{\ln(x)}{\sin(x)})

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