Question

∫xe^（x/2）dx

Answer 1

用分部积分法

∫xe^(x/2)dx

=2∫xe^(x/2)d(x/2)

=2∫xde^(x/2)

=2xe^(x/2)-2∫e^(x/2)dx

=2xe^(x/2)-4∫e^(x/2)d(x/2)

=2xe^(x/2)-4e^(x/2)+C

=(2x-4)e^(x/2)+C

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