求一道高数题? P77.10

2025-06-28 07:22:35
推荐回答(1个)
回答1:

作变量代换 x=t^6,则 dx = 6t^5 dt,
原式 = ∫6t^5 / (t^3+t^2) dt
=∫6t^3 / (t+1) dt
=6∫(t^2-t+1 - 1/(t+1))dt
=2t^3 - 3t^2 + 6t - 6ln(t+1)+C
=(回代即可)