Question

急,求不定积分In(x^2+1)dx ∫下面是0 上面是3

Answer 1

∫(0,3)ln(x²+1)dx

=xln(x²+1)|(0,3)－∫(0,3)xdln(x²+1)

=3ln10－∫(0,3)2x²/(x²+1)dx

=3ln10－2∫(0,3)(x²+1－1)/(x²+1)dx

=3ln10－2∫(0,3)[1－1/(x²+1)]dx

=3ln10－2∫(0,3)dx+2∫(0,3)1/(x²+1)dx

=3ln10－6+2arctan3.