integral 2x^2 √4x^3-5 dx

jawab

∫ (2x²)√(4x³ - 5) dx

u = 4x³ - 5
du = 12x² dx
2x² dx = 1/6 du

∫(2x²)√(4x³-5) dx = 1/6 ∫u^(1/2) du
= 1/6 (2/3) (u)^(-1/2) + c
= (1/9) (1/√u) +c
=(1/9)(1/u )√u+ c
= 1/{9(4x³ -5)} √(4x³-5)
= {√(4x³ -5)} / {9(4x³ -5)}

[tex] =\, \frac{ \sqrt{4x^3 -5} }{36x^3 - 45}\, + \, c[/tex]