Question

求x/根号下(1+x) 在8到3的定积分

Answer 1

=∫(x+1-1)/根号（1+x)dx

=∫根号（x+1)dx-∫1/根号（1+x)dx

=2/3(x+1)^(3/2)-2(1+x)^(1/2)

=2/3(3+1)^(3/2)-2/3(8+1)^(3/2)-2(1+3)^(1/2)+2(1+8)^(1/2)

=2/3*8-2/3*27-4+6

=16/3-18-4+6

=16/3-16

=-32/3