Question

求不定积分∫x^3 dx/(9+x^2) （同济六版208页第32题）

Answer 1

令x^2=t

∫x^3/9+x^2 dx=1/2∫x^2/(9+x^2)dx^2

=1/2∫tdt/(9+t)

=1/2∫(9+t-9)dt/(9+t)

=1/2∫dt-9/2∫dt/9+t

=t/2-9In(9+t)/2

=x^2/x-(9/2)In(9+x^2)+C

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