Помогите, пожалуйста, найти интегралы:
1) int (x^2 + 1) * (x^2 - 2)/x^(2/3) dx
2) int sec^2 x dx

1) int (x^2 + 1) * (x^2 - 2)/x^(2/3) dx = int (x^4 - x^2 - 2)/x^(2/3) dx =
= int (x^(4 - 2/3) - x^(2 - 2/3) - 2 * x^(-2/3)) dx =
= int (x^(10/3) - x^(4/3) - 2 * x^(-2/3)) dx =
= 1/(10/3 + 1) * x^(10/3 + 1) - 1/(4/3 + 1) * x^(4/3 + 1) -
- 2 * 1/(-2/3 + 1) * x^(-2/3 + 1) + C =
= 3/13 * x^(13/3) - 3/7 * x^(7/3) - 6 * x^(1/3) + C =
= 3/13 * x^(12/3 + 1/3) - 3/7 * x^(6/3 + 1/3) - 6 * x^(1/3) + C =
= 3/13 * x^4 * x^(1/3) - 3/7 * x^2 * x^(1/3) - 6 * x^(1/3) + C =
= x^(1/3) * (3/13 * x^4 - 3/7 * x^2 - 6) + C
2) int sec^2 x dx = int (sec x)^2 dx = int (1/cos x)^2 dx = int 1/cos^2 x dx =
= tg x + C