Square Root Question

  • Thread starter ralfsk8
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  • #1
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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
 

Answers and Replies

  • #2
Mentallic
Homework Helper
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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 [tex]\sqrt{4a+b}[/tex] then in order to make the coefficient of a equal to 1, just factor out a 4 and then use the rule that [itex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/itex] so we'll have

[tex]\sqrt{4a+b}[/tex]
[tex]=\sqrt{4(a+b/4)}[/tex]
[tex]=\sqrt{4}\sqrt{a+b/4}[/tex]
[tex]=2\sqrt{a+b/4}[/tex]
 

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