Задача 46229 ...

hardboy

2020-04-06 22:37:53

∫ dx/ sqrt(x^2-10x+26)

sova

2020-04-06 22:56:42

Так как x^2-10x+26=x^2-10x+25+1=(x-5)^2+1

и

[m] \int \frac{dx}{\sqrt{x^2+1}}=ln|x+\sqrt{x^2+1}+C[/m], то

[m] \int \frac{dx}{\sqrt{(x-5)^2+1}}=\int \frac{d(x-5)}{\sqrt{(x-5)^2+1}}=ln|x-5+\sqrt{x^2-10+26}|+C[/m]