[tex]\int \frac{x+5}{\sqrt{x+4}} dx = \\x+4=t^2\\dx=2tdt\\=\int \frac{(t^2+1)2t}{t} dt = 2\int (t^2+1) dt = \frac{2t^3}{3}} +2t +c = \\= \frac{2(x+4)^{3/2}}{3}} +2(x+4)^{1/2} +c[/tex]
[tex]\int (9x^2+2)lnx dx = \\u=lnx \\ du = \frac{1}{x}dx \\dv= (9x^2+2)dx \\v = 3x^3+2x\\=(3x^3+2x)lnx - \int \frac{1}{x} (3x^3+2x)dx=\\= (3x^3+2x)lnx - \int (3x^2+2)dx=\\\\= (3x^3+2x)lnx -x^3-2x+c[/tex]
