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# Integration

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1. Why do we use integration by parts?
2. Because otherwise you can't solve lots of integrals*
3. (Original post by Wahrheit)
Because otherwise you can't solve lots of integrals*
Yepp this
4. It is mostly used for, but not limited to products. So stuff like that most of the time.
5. It's the reverse of the product rule for differentiation. This can be shown but I could never be bothered. Look it up.
6. (Original post by English-help)
Why do we use integration by parts?
To integrate things.
7. (Original post by English-help)
Why do we use integration by parts?
Because we think it may help us!

As noted above, the product rule for differentiation tells us that

(uv)' = u'v + uv'

where the ' denotes differentiation with respect to x.

So we can integrate both sides of this, and hope that one of the 2 integrals on the right can be done more simply than the other.

The trick is thinking about which function in a product to take as the 'first' one and which as the 'second'. Generally speaking, differentiation simplifies polynomials and either leaves exponential and trig functions alone or converts them to other exponential and trig functions, possibly multiplied by a constant.
8. (Original post by Zacken)
To integrate things.
If we had the integral of x^3lnx we would make u=lnx as we cant integrate lnx right?
9. (Original post by English-help)
If we had the integral of x^3lnx we would make u=lnx as we cant integrate lnx right?
We can integrate , just not in a nice form compatible with IBP, so yes - we would make .
10. To swap a hard integral, or in fact an impossible integral, for an easier one. Simple as that.

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