Integral of x*arcctg(x/5) dx
The solution
The answer (Indefinite)
[src]
/ /x\ 2 /x\
| 25*acot|-| x *acot|-|
| /x\ 5*x \5/ \5/
| x*acot|-| dx = C + --- + ---------- + ----------
| \5/ 2 2 2
|
/
$$\int x \operatorname{acot}{\left(\frac{x}{5} \right)}\, dx = C + \frac{x^{2} \operatorname{acot}{\left(\frac{x}{5} \right)}}{2} + \frac{5 x}{2} + \frac{25 \operatorname{acot}{\left(\frac{x}{5} \right)}}{2}$$
5 25*pi
- + 13*acot(1/5) - -----
2 4
$$- \frac{25 \pi}{4} + \frac{5}{2} + 13 \operatorname{acot}{\left(\frac{1}{5} \right)}$$
=
5 25*pi
- + 13*acot(1/5) - -----
2 4
$$- \frac{25 \pi}{4} + \frac{5}{2} + 13 \operatorname{acot}{\left(\frac{1}{5} \right)}$$
5/2 + 13*acot(1/5) - 25*pi/4
Use the examples entering the upper and lower limits of integration.