Question

∫x^2/（a^2-x^6）dx＝?

Answer 1

∫ x²/(a² - x⁶) dx

= ∫ 1/[a² - (x³)²] d(x³/3)

= (1/3)∫ 1/[(a - x³)(a + x³)] d(x³)

= (1/3)[1/(2a)]∫ [(a + x³) + (a - x³)]/[(a - x³)(a + x³)] d(x³)

= [1/(6a)]∫ [1/(a - x³) + 1/(a + x³)] d(x³)

= [1/(6a)] * [- ln|a - x³| + ln|a + x³|] + C

= [1/(6a)]ln|(a + x³)/(a - x³)| + C