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Popular Calculus Problems

integral of 1/(36x^2+1)	\int\:\frac{1}{36x^{2}+1}dx
derivative of-4xy	\frac{d}{dx}(-4xy)
(\partial)/(\partial y)(y/(1+x^2+y^2))	\frac{\partial\:}{\partial\:y}(\frac{y}{1+x^{2}+y^{2}})
derivative of cx^{-4}	\frac{d}{dx}(cx^{-4})
sum from n=1 to infinity of 3(5)^{-n}	\sum\:_{n=1}^{\infty\:}3(5)^{-n}
limit as x approaches 0 of 9x-8sqrt(x)	\lim\:_{x\to\:0}(9x-8\sqrt{x})
integral from 0 to 1/4 of arcsin(2x)	\int\:_{0}^{\frac{1}{4}}\arcsin(2x)dx
derivative of (5x/(x^2-1))	\frac{d}{dx}(\frac{5x}{x^{2}-1})
derivative of y=cos^4(x)	derivative\:y=\cos^{4}(x)
limit as h approaches 0 of 3x^2+2xh+h^2	\lim\:_{h\to\:0}(3x^{2}+2xh+h^{2})
integral of 20xln(x)	\int\:20x\ln(x)dx
limit as x approaches 0 of (sin(8x))/(sin(7x))	\lim\:_{x\to\:0}(\frac{\sin(8x)}{\sin(7x)})
(\partial)/(\partial x)(arccos(y/x))	\frac{\partial\:}{\partial\:x}(\arccos(\frac{y}{x}))
integral of (6x^2-5x+3)	\int\:(6x^{2}-5x+3)dx
(dy)/(dx)=(y(xy^3-1))	\frac{dy}{dx}=(y(xy^{3}-1))
integral of cos(x)cos(2x)cos(3x)	\int\:\cos(x)\cos(2x)\cos(3x)dx
derivative of e^{-8x^2}	\frac{d}{dx}(e^{-8x^{2}})
derivative of 3/(3x-5)	\frac{d}{dx}(\frac{3}{3x-5})
integral of 1/(5x^2-20x+100)	\int\:\frac{1}{5x^{2}-20x+100}dx
integral of 5/(sec(x)-1)	\int\:\frac{5}{\sec(x)-1}dx
area x^2-4x,x0,[-2,4]	area\:x^{2}-4\cdot\:x,x\cdot\:0,[-2,4]
derivative of g(x)=6x^2e^{-x}	derivative\:g(x)=6x^{2}e^{-x}
integral of (8x-4)	\int\:(8x-4)dx
limit as x approaches 1 of e^{3x^3-3x}	\lim\:_{x\to\:1}(e^{3x^{3}-3x})
derivative of 26	derivative\:26
integral of sin(2x)sin(4x)	\int\:\sin(2x)\sin(4x)dx
taylor sin(1/x)	taylor\:\sin(\frac{1}{x})
limit as x approaches 0+of (ln(x))/(sqrt(x))	\lim\:_{x\to\:0+}(\frac{\ln(x)}{\sqrt{x}})
y^{''}+2y^'+5y=4cos(2t)e^{-t}	y^{\prime\:\prime\:}+2y^{\prime\:}+5y=4\cos(2t)e^{-t}
integral of 1/(cos^5(x))	\int\:\frac{1}{\cos^{5}(x)}dx
derivative of 2/(x^{1/3)}-2	derivative\:\frac{2}{x^{\frac{1}{3}}}-2
2y^'+ty=7	2y^{\prime\:}+ty=7
derivative of (3x-1/(2x+5))	\frac{d}{dx}(\frac{3x-1}{2x+5})
derivative of f(x)=7^x	derivative\:f(x)=7^{x}
laplacetransform 2/3 t^3*e^{-8t}	laplacetransform\:\frac{2}{3}t^{3}\cdot\:e^{-8t}
derivative of 4/(x^2-2/x)	\frac{d}{dx}(\frac{4}{x^{2}}-\frac{2}{x})
(\partial)/(\partial x)(3y^2+20x^2y^3)	\frac{\partial\:}{\partial\:x}(3y^{2}+20x^{2}y^{3})
laplacetransform cos^2(pit)	laplacetransform\:\cos^{2}(πt)
f^'(x)= 9/(2sqrt(9x-5))	f^{\prime\:}(x)=\frac{9}{2\sqrt{9x-5}}
integral of sqrt(4x-3)	\int\:\sqrt{4x-3}dx
integral of (x+5)/((x+3)(x-2)^2)	\int\:\frac{x+5}{(x+3)(x-2)^{2}}dx
(dy)/(dt)-2ty=-12t^2e^{t^2},y(0)=-1	\frac{dy}{dt}-2ty=-12t^{2}e^{t^{2}},y(0)=-1
integral of (ln(4x))^2	\int\:(\ln(4x))^{2}dx
yy^'+x=0	yy^{\prime\:}+x=0
integral of (sqrt(r)+3)/(r+3)	\int\:\frac{\sqrt{r}+3}{r+3}dr
integral of (82x+8)/((9x+1)(x-1))	\int\:\frac{82x+8}{(9x+1)(x-1)}dx
9(t+1)((dy)/(dt))-6y=18t	9(t+1)(\frac{dy}{dt})-6y=18t
derivative of (17)/x	derivative\:\frac{17}{x}
(\partial)/(\partial x)((x-1)^2)	\frac{\partial\:}{\partial\:x}((x-1)^{2})
inverse oflaplace 3/((s-7)^4)	inverselaplace\:\frac{3}{(s-7)^{4}}
integral of arctan(8t)	\int\:\arctan(8t)dt
(\partial)/(\partial x)(x/A)	\frac{\partial\:}{\partial\:x}(\frac{x}{A})
integral of x/(x+9)	\int\:\frac{x}{x+9}dx
integral of (2x)/(cos^2(x))	\int\:\frac{2x}{\cos^{2}(x)}dx
integral of 9cot^4(x)	\int\:9\cot^{4}(x)dx
derivative of (2x-7^{-1}(x+5))	\frac{d}{dx}((2x-7)^{-1}(x+5))
derivative of y=(2x+3)/(5x-1)	derivative\:y=\frac{2x+3}{5x-1}
implicit (dy)/(dx),sin(xy^3)=y^3	implicit\:\frac{dy}{dx},\sin(xy^{3})=y^{3}
derivative of 5-6x	\frac{d}{dx}(5-6x)
sum from n=1 to infinity of n/(5n+1)	\sum\:_{n=1}^{\infty\:}\frac{n}{5n+1}
simplify ln(k/l)	simplify\:\ln(\frac{k}{l})
limit as x approaches-4 of 4+x	\lim\:_{x\to\:-4}(4+x)
y^{''}+y= 1/4 cos(3t)	y^{\prime\:\prime\:}+y=\frac{1}{4}\cos(3t)
integral of x^3sqrt(81-x^2)	\int\:x^{3}\sqrt{81-x^{2}}dx
integral of (cos(3x))/(sin(3x))	\int\:\frac{\cos(3x)}{\sin(3x)}dx
integral of 1/((u^2+a^2)^2)	\int\:\frac{1}{(u^{2}+a^{2})^{2}}du
y^{''}+10y^'+26y=0	y^{\prime\:\prime\:}+10y^{\prime\:}+26y=0
derivative of f(x)=x^2sqrt(9-x^2)	derivative\:f(x)=x^{2}\sqrt{9-x^{2}}
x^4+y^3sqrt(x^5+3)y^'=0	x^{4}+y^{3}\sqrt{x^{5}+3}y^{\prime\:}=0
derivative of x^2(x+7^3)	\frac{d}{dx}(x^{2}(x+7)^{3})
x(dy)/(dx)+2y=10x^2	x\frac{dy}{dx}+2y=10x^{2}
derivative of arctan(3x+2)	\frac{d}{dx}(\arctan(3x+2))
integral of (2e^{2x})/(e^{2x)+8e^x+15}	\int\:\frac{2e^{2x}}{e^{2x}+8e^{x}+15}dx
integral of 5arctan(2y)	\int\:5\arctan(2y)dy
integral of x^3ln(3x)	\int\:x^{3}\ln(3x)dx
integral of sin(ln(5x))	\int\:\sin(\ln(5x))dx
derivative of (-x^2+2/((x^2+2)^2))	\frac{d}{dx}(\frac{-x^{2}+2}{(x^{2}+2)^{2}})
derivative of (x^{1/3}-4)/(x^{7/2)}	derivative\:\frac{x^{\frac{1}{3}}-4}{x^{\frac{7}{2}}}
integral of (z(1-z))/((z+1)(z^2+1)^2)	\int\:\frac{z(1-z)}{(z+1)(z^{2}+1)^{2}}dz
integral from 0 to t of e^xsin(t-x)	\int\:_{0}^{t}e^{x}\sin(t-x)dx
(dy)/(dt)+y=5sin(2t)	\frac{dy}{dt}+y=5\sin(2t)
integral from 0 to 4 of x/(sqrt(x^2+9))	\int\:_{0}^{4}\frac{x}{\sqrt{x^{2}+9}}dx
limit as x approaches+0 of ln(x^2)	\lim\:_{x\to\:+0}(\ln(x^{2}))
inverse oflaplace (2s+1)/(2s^2+s+1)	inverselaplace\:\frac{2s+1}{2s^{2}+s+1}
integral of (2sin^3(sqrt(x)))/(sqrt(x))	\int\:\frac{2\sin^{3}(\sqrt{x})}{\sqrt{x}}dx
y^'+y=te^t	y^{\prime\:}+y=te^{t}
y^{''}+16y=2sin(2t)	y^{\prime\:\prime\:}+16y=2\sin(2t)
derivative of sqrt(x^2-5)	\frac{d}{dx}(\sqrt{x^{2}-5})
limit as x approaches infinity of ax^4+bx^2+c	\lim\:_{x\to\:\infty\:}(ax^{4}+bx^{2}+c)
integral of 1/(x^4sqrt(x^2-3))	\int\:\frac{1}{x^{4}\sqrt{x^{2}-3}}dx
derivative of 2cos(4x)	\frac{d}{dx}(2\cos(4x))
integral of 11tan^4(x)sec^6(x)	\int\:11\tan^{4}(x)\sec^{6}(x)dx
integral of ((4x)/y)	\int\:(\frac{4x}{y})dx
(dy)/(dx)=x-y	\frac{dy}{dx}=x-y
derivative of (4x)/(3-tan(x))	derivative\:\frac{4x}{3-\tan(x)}
limit as x approaches 0 of (sin(7x))/x	\lim\:_{x\to\:0}(\frac{\sin(7x)}{x})
derivative of 1-tan(x)	\frac{d}{dx}(1-\tan(x))
laplacetransform f(t)=te^{4t}	laplacetransform\:f(t)=te^{4t}
derivative of xln(x/5)	\frac{d}{dx}(x\ln(\frac{x}{5}))
derivative of 1/2 bh	derivative\:\frac{1}{2}bh

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