Solve ∫(e^x)/(√4-e^(2x)) w/ arcsin of x

[ralfsk8]

Homework Statement

∫(e^x)/(√4-e^(2x))

Homework Equations

arcsin of x

The Attempt at a Solution

I know how the problem should be solved and have an idea of what the final answer will be. My only question is, how would I take out the four from the square root, in order to make it a 1? Can I just pull out 1/4?

Thank You

 

[Mentallic]

Homework Statement

∫(e^x)/(√4-e^(2x))

Homework Equations

arcsin of x

The Attempt at a Solution

I know how the problem should be solved and have an idea of what the final answer will be. My only question is, how would I take out the four from the square root, in order to make it a 1? Can I just pull out 1/4?

Thank You

Yep. If you have $$\sqrt{4a+b}$$ then in order to make the coefficient of a equal to 1, just factor out a 4 and then use the rule that $\sqrt{ab}=\sqrt{a}\sqrt{b}$ so we'll have

$$\sqrt{4a+b}$$
$$=\sqrt{4(a+b/4)}$$
$$=\sqrt{4}\sqrt{a+b/4}$$
$$=2\sqrt{a+b/4}$$