integral (x+1) √x pangkat 2+2x-1 dx

Penyelesaian: 

Misal: y = x² + 2x - 1

∫ [tex](x + 1)( \sqrt{x^2 + 2x -1)} dx[/tex]

dy / dx = 2x + 2
dx = dy / 2x + 2

∫ [tex](x + 1)(y)^1/2 \frac{dy}{(2x + 2)} [/tex]
= [tex] \frac{1}{2}[/tex] ∫ [tex]y^1/2 dy[/tex]
= [tex] \frac{1}{2} . \frac{2}{3} y^3/2 + c[/tex]
= [tex] \frac{1}{3} y \sqrt{y} + c[/tex]
= [tex] \frac{1}{3}(x^2 + 2x - 1) \sqrt{x^2 + 2x - 1} + c[/tex]