Question

Вычислить интеграл
∫$frac{7dx}{ x^{3} + x^{2}}$

Answer 1

7/(x^3 + x^2) = 7*( (-1/x) + (1/x^2) + (1/(x+1) ) ).
S (7dx/(x^3+x^2) ) = 7*(-ln|x| -(1/x) + ln|x+1| ) +C=
= 7*( ln|(x+1)/x| - (1/x) ) +C = 7*ln| 1 + (1/x) | - (7/x) +C.