Question

Qual a integral de (1/raiz de x)+(x raiz de x/3) dx

Answer 1

Resposta:

Se for  ∫ 1/√x  +(x*√x)/3  dx

Observe ==>x*√x =√(x²*x) =√x³ =x^(3/2)

∫ x^(-1/2) +x^(3/2)/3  dx

= [x^(-1/2+1)]/(-1/2+1) +(1/3)* [x^(3/2+1)]/(3/2+1)   + constante

= [x^(1/2)]/(1/2) +(1/3)* [x^(5/2)]/(5/2)   + constante

= 2*[x^(1/2)] +(2/15)* [x^(5/2)]  + constante

= 2*√x + (2/15)* √x⁵  + constante