Question

o valor da integral ∫ x³ lnx dx é?

Answer 1

Resposta:

∫ x³ lnx dx

Método por Partes

u = ln(x)  ==> du =(1/x) * dx

x³ dx =dv  ==> ∫x³dx= ∫dv  ==> x⁴/4 = v

∫ x³ lnx dx = ln(x) * x⁴/4 - ∫ x⁴/4 * (1/x) * dx

∫ x³ lnx dx = ln(x) * x⁴/4 - (1/4) * ∫ x³ * dx

∫ x³ lnx dx = ln(x) * x⁴/4 - (1/4) * x⁴/4 + constante

∫ x³ lnx dx = ln(x) * x⁴/4 -  x⁴/16 + constante

∫ x³ lnx dx = x⁴//16 * [4*ln(x) -1]  + constante