不定积分 ∫x대⼀(9+x눀)dx的解答过程

2024-12-04 21:15:40
推荐回答(2个)
回答1:

∫x³/(9+x²)dx

= ∫(x³+9x-9x)/(9+x²)dx
=∫xdx-9∫x/(9+x²)dx
=x²/2-9/2∫1/(9+x²)d(9+x²)
=x²/2-9/2ln(9+x²)+c

回答2:

解:
=0.5 ∫x²/(9+x²)dx²
=0.5( ∫1-(9/(9+x²))dx²
=0.5 x²- ∫9/(9+x²)dx²
=0.5 x²-9ln(9+ x²)+c