Can substitution help solve this improper integral?

[regnar]

I've been stuck on this problem for quite some time and I get as far as setting up the problem. They are asking me to evaluate this integral:

$$\int_0^1{\frac{(6ln4x)}{\sqrt{x}}dx$$ and I get as far as:

$$\lim_{b \to 0^+}{6\int_b^1{\frac{(ln4x)}{\sqrt{x}}$$

 

[Count Iblis]

Substituting x = t^2 seems to work...

 

[regnar]

I'm not sure what you mean or where $$t^2$$ came from.

 

[njama]

It's called substitution.

The substitution is $$t=\sqrt{x}$$ or $$t^2 = x$$