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- Integral of d{x}:
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Integral of e^3
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Integral of 4*x*exp(x^2)
- Integral of tan^(-1)x
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Integral of x*2^x
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Identical expressions
- xarcctg(x/ three)
- xarcctg(x divide by 3)
- xarcctg(x divide by three)
- xarcctgx/3
- xarcctg(x/3)dx
Integral of xarcctg(x/3) dx
The solution
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[src]
___ \/ 3 / | | /x\ | x*acot|-| dx | \3/ | / 0
$$\int\limits_{0}^{\sqrt{3}} x \operatorname{acot}{\left(\frac{x}{3} \right)}\, dx$$
Integral(x*acot(x/3), (x, 0, sqrt(3)))
The answer (Indefinite)
[src]
/ /x\ 2 /x\ | 9*acot|-| x *acot|-| | /x\ 3*x \3/ \3/ | x*acot|-| dx = C + --- + --------- + ---------- | \3/ 2 2 2 | /
$$\int x \operatorname{acot}{\left(\frac{x}{3} \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(\frac{x}{3} \right)}}{2} + \frac{3 x}{2} + \frac{9 \operatorname{acot}{\left(\frac{x}{3} \right)}}{2}$$
The graph
The answer
[src]
___ pi 3*\/ 3 - -- + ------- 4 2
$$- \frac{\pi}{4} + \frac{3 \sqrt{3}}{2}$$
=
=
___ pi 3*\/ 3 - -- + ------- 4 2
$$- \frac{\pi}{4} + \frac{3 \sqrt{3}}{2}$$
-pi/4 + 3*sqrt(3)/2
Use the examples entering the upper and lower limits of integration.