Question

Прошу решить:
|dx/(x^2+6x-7)
Где | - интеграл

Answer 1

x²+6x-7=0
x1+x2=-6 U x1*x2=-7⇒x1=-7 U x2=1
1/(x²+6x-7)=A/(x+7)+B/(x-1)
Ax-A+Bx+7B=1
A+B=0⇒A=-B
7B-A=1⇒7B+B=1⇒8B=1⇒B=1/8
A=-1/8
1/(x²+6x-7)=1/8(1-x)+1/8(x+7)
Sdx/(x²+6x-7)=1/8Sdx/(1-x)-1/8Sdx/(x+7)=1/8(ln(1-x)-ln(x+7))