tentukan integral √3x+2dx

3/2 X^2 + 2 X + C
semoga bisa membantu

v= 3x + 2
[tex] \frac{dv}{dx} [/tex] = 3
dx = [tex] \frac{dv}{3} [/tex]

∫√(3x + 2) dx = ∫√v dx = ∫[tex] v^{ \frac{1}{2} } [/tex] [tex] \frac{dv}{3} [/tex]
                                   = 1/3 ∫ [tex] v^{ \frac{1}{2} } [/tex] dv
                                       1      [tex] v^{ \frac{3}{2} } [/tex]
                                   = --- x -----
                                       3     3/2
                                     
                                   =  2/9 (3x + 2)^[tex] \frac{3}{2} [/tex] + c
                                   =  2/9 (3x + 2) (3x +2)^[tex] \frac{1}{2} [/tex] + c
                                   =  2/9 (3x + 2) √(3x + 2) + c