Question

Use a técnica de integração por partes e calculeS x3logxdx

Answer 1

∫ x³ * logx dx

Fazendo por partes:

u = log x ==>du =(1/x) dx

x³ dx = dv ==> ∫ x³ dx = ∫ dv ==> x⁴/4 = v

∫ x³ * logx dx = (1/4) * x⁴ * log x - ∫ x⁴/4 * (1/x) dx

∫ x³ * logx dx = (1/4) * x⁴ * log x - ∫ x³/4 dx

∫ x³ * logx dx = (1/4) * x⁴ * log x - (1/4) * x⁴/4

∫ x³ * logx dx = (1/4) * x⁴ * log x - x⁴/16

∫ x³ * logx dx = (x⁴/16) * (4log x -1) + const