Question

Integral raiz quadrada de x lnxdx

Answer 1

Resposta:

∫√x * ln(x) dx

Fazendo por Partes

u= ln(x)   ==>du=(1/x) * dx

dv =√x dx  ==> ∫ dv =∫ √x dx ==>v= x^(1/2+1) /(1/2+1) =(2/3)* x^(3/2)

∫√x * ln(x) dx =(2/3)* x^(3/2) * ln(x) - ∫ (2/3)* x^(3/2) (1/x) * dx

∫√x * ln(x) dx =(2/3)* x^(3/2) * ln(x) - (2/3)*∫ x^(3/2-1) * dx

∫√x * ln(x) dx =(2/3)* x^(3/2) * ln(x) - (2/3)*∫ x^(1/2) * dx

∫√x * ln(x) dx =(2/3)* x^(3/2) * ln(x) - (2/3)* x^(1/2+1)  /(1/2+1) + c

∫√x * ln(x) dx =(2/3)* x^(3/2) * ln(x) - (2/3)* x^(3/2)  /(3/2) + c

∫√x * ln(x) dx =(2/3)* √x³ * ln(x) - (4/9)* x^(3/2)   + c