integrate e^(2x) / (e^(4x) + 9)

am I allowed to simplify the e^(2x) with the e^(4x)?

Thank you

yes. let u = e^2x

Then du = 2e^2x dx and you have 1/(u^2+9) du/2

And proceed from there

thanks steve!

Yes, you are allowed to simplify the expression e^(2x) with e^(4x) by using the properties of exponents.

To simplify this expression, you can rewrite it as e^(2x) / (e^(4x) + 9) = 1 / (e^(4x)/e^(2x) + 9).

Using the rule of exponents which states that e^(a+b) = e^a * e^b, we can simplify e^(4x)/e^(2x) as e^(2x).

Therefore, the simplified expression becomes 1 / (e^(2x) + 9).

Now, you can proceed to integrate the expression 1 / (e^(2x) + 9) by using the techniques of calculus.