Question

o valor da integral ∫$\frac{ x^{3} }{(5 x^{4}+2) ^{3} }$ dx é:

Answer 1

Boa noite Walder

∫ x³/(5x⁴ + 2)³ dx

 fazendo u = 5x⁴  + 2 e du = 20x³ dx

∫ x³/(5x⁴ + 2)³  = 1/20 ∫ 1/u³ du

∫ 1/u³ = -1/(2u²)

1/20 ∫ 1/u³ du= -1/(40u²) + C

u = 5x⁴ + 2

∫ x³/(5x⁴ + 2)³= -(5x⁴ + 2)²/40 + C