integration

Question

can anyone solve these two please? when i change the first expression to the second one prior to integration, i get a different result than directly integrating the first expression!

 

First integration: x^(-0.5)/(√x+0.5) dx

 

Second integration: dx/(1+0.5*sqrt(x))

Answer 1

In the numerator, X^(-0.5) is equal to 1/sqrt(x)

 

Therefore, in the denominator, sqrt(X) times sqrt(X) => X, not 1.

 

The second integration should therefore be of 

 

dx/ (x + 0.5*sqrt(x))