“What are some tips on how to solve Integration problems using U-Substitution?”

Question from Quora

u-sub-integration-1

There are basically two terms here, the 5x and the 1- x^2 in parentheses.

The general idea for u-substitution is to make u something that when you take the derivative of it can be substituted for what is left over (with a little manipulation).

So if you chose 5x as your u, then du would be 5dx which you could not easily substitute.

If what you choose seems to not be working, either you made a mistake or you should try a different option.

For this problem choosing u = 1 -x^2 seems to work better. You can probably even take the derivative of that in your head to figure out in advance if it will work well.

u-sub-integration-2

At that point it becomes much easier to solve.

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