xsquare root2x9dxSolutionintegralx2x9dx put 2x9t xt92 and dx

Solution

integral(x((2x+9)))dx

put 2x+9=t

==>x=(t-9)/2 and dx=dt/2

integral(x((2x+9)))dx

=integral((t-9)(t))dt/4

=integral((t^(3/2)-9t))dt/4

=(2t^(5/2) /5 -6t^(3/2)))/4+c

=(2( 2x+9)^(5/2) /5 -6( 2x+9)^(3/2)))/4+c