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i was thinking of this,
multiplying and dividing by e^(-x)
would work on paper to see whether it works...
from what i saw in the solution, it looks like they multiplied and divided by e^x, but i thought we couldnt do that? we can only multioply by a constant
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we CAN multiply and divide by a function too,
like e^x or e^(-x) ...
we can do that??!!! I though it was only by a constant.
if we can multiply and divide by a function, then the integral becomes really easy. Thanks.
So i can also multipy and divide by x??
why you want to do that ?
and now i think, substituting , u = 1+e^(2x) would beeasier.
i mean, not for this integral, but lets say for a different integral, i could possibly divdie and multiply by x?
if that makes the finding the integral easier, then YES, you can do that
Okay, thank you.
Another way: If you've learned trigonometric substitutions, you could rewrite the integral first using
Then use \(u=\tan t~\Rightarrow~du=\sec^2t~dt\).