Question

∫ln(x+1)/√x+1dx求不定积分

Answer 1

∫ln(x+1)/√(x+1)dx

=∫ln(x+1)/√(x+1)d(x+1)

=2∫ln(x+1)d√(x+1)

=2√(x+1) ln(x+1)-2∫√(x+1) * 1/(x+1) dx

=2√(x+1) ln(x+1)-2∫ dx/√(x+1)

=2√(x+1) ln(x+1)-4√(x+1) +C