Because the objective here is to get rid of the radical, you need to find a function that makes the
expression under the radical a square. If you put , then the expression under the radical
becomes , but gives
which is equal to and ... it gets rid of the (the other one doesn't).
It's just a substitution that works and makes an alternative to partial fractions. Whenever you have
integral of the form , you can let or (doesn't matter which).
You have . Differentiating it with respect to using the quotient rule, we have:Neither do I get this part: ?!
It seems like you pulled it out of thin air. Where did the 7 and (x + 1)^2 come from?
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