Hello find
finde ∫_0 ^(+∞) ((ln(x))/(x^2 +ax+b))dx
conditions a^2 <4b
in therm of x_1 ,x_2 root of X^2 +aX+b
hint Residus theorem applied too ((log^2 (z))/(z^2 +az+b))
this is very usufull i find it in lecture yesterday
because we can easly evaluat any kinde of ∫_0 ^(+∞) ((log^k (z))/(p(z)))dz
withe p(z) eiwthout root in ]0,+∞[ deg(p(z))≥2
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