Question

Нужно найти неопределенный интеграл.​

Answer 1

$\displaystyle \int\limits\dfrac{1-5x}{1+25x^2}dx=\int\limits\dfrac{1}{1+(5x)^2}dx-\int\limits\dfrac{5x}{1+25x^2}dx=\int\limits\dfrac{dx}{1+(5x)^2}-\\ \\ \\ -\dfrac{1}{10}\int\limits\dfrac{d(1+25x^2)}{1+25x^2}=\dfrac{1}{5}{\rm arctg}5x-\dfrac{1}{10}\ln\left(1+25x^2\right)+C$