DiaThesadmad
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Evaluating integral In
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Dr.Peterson
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I'll make it easier to read:
Please show us the entire question (and translate it) in case there is something important you have omitted by cropping it. I'm wondering whether it is meant to be proved by induction, for example.
Then please show your work on integration by parts, in case you made a mistake in it.
Please show us the entire question (and translate it) in case there is something important you have omitted by cropping it. I'm wondering whether it is meant to be proved by induction, for example.
Then please show your work on integration by parts, in case you made a mistake in it.
HallsofIvy
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Is the problem to find \(\displaystyle I_n= \int_{-1/2}^{1/2} \frac{x- 1}{(x+ 1)^n}dx\) for all n, as appears?
If so then, as Dr. Peterson suggests, it might be simplest to calculate the first few integrals, say \(\displaystyle I_1\), \(\displaystyle I_2\), and \(\displaystyle I_3\), guess a general formula, then use "proof by induction to prove that formula is correct.
Of course you will want to use "integration by parts" at each step. I would suggest trying \(\displaystyle dv= \frac{x-1}{(x+1)^{n-1}}dx\), \(\displaystyle u= \frac{1}{x+1}\).
If so then, as Dr. Peterson suggests, it might be simplest to calculate the first few integrals, say \(\displaystyle I_1\), \(\displaystyle I_2\), and \(\displaystyle I_3\), guess a general formula, then use "proof by induction to prove that formula is correct.
Of course you will want to use "integration by parts" at each step. I would suggest trying \(\displaystyle dv= \frac{x-1}{(x+1)^{n-1}}dx\), \(\displaystyle u= \frac{1}{x+1}\).