# Solutions to Problem Set 8

Math 211-03

9-19-2017

[Integration techniques]

1. Compute .

Let . I get , so .

Let . I get .

Then

Let . I get , so .

So

2. Compute .

Notice that

So

3. Compute .

4. Compute .

5. Compute .

6. Compute .

7. Compute .

Let . I get

Differentiate the last x-equation:

Let . I get

Differentiate the last x-equation:

Let . I get

Plugging this into gives

Differentiate the last x-equation:

Plug into to get .

Therefore,

Here's the work for the second term in the integral:

To think is not enough; you must think of something. - Jules Renard

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