求不定积分∫xln(1+x^2)dx

首页/题库/496℃/2024-05-19 19:52:25

优质解答：

∫xln(1+x^2)dx

=1/2∫ln(1+x^2)dx^2

=1/2∫ln(1+x^2)d(1+x^2)

=1/2(1+x^2)ln(1+x^2)-1/2∫(1+x^2)dln(1+x^2)

=1/2(1+x^2)ln(1+x^2)-1/2∫(1+x^2)*1/(1+x^2)d(1+x^2)

=1/2(1+x^2)ln(1+x^2)-1/2∫dx^2

=1/2(1+x^2)ln(1+x^2)-1/2x^2+C

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