Question

Решите неопределенный$intlimits{arctg sqrt{7-x} } , dx$ интеграл по частям.

Answer 1

$displaystyle ...=bigg{ sqrt{7-x} =ubigg}=-2intlimits {ucdot arctgu} , du=-u^2arctgu+intlimits { frac{u^2du}{u^2+1} } , =\ \ \ =-u^2arctgu-arctgu+u+C=\ \ \ = sqrt{7-x} +(x-7)arctg sqrt{7-x} -arctg sqrt{7-x} +C$