大师作文网∫x^2/（a^2-x^6）dx＝?
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∫x^2/（a^2-x^6）dx＝?
∫ 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
= ∫ 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
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