Answers to question 4.1.22 all subparts

Answer to 4.1.22 (a) :

In this question, we have to transform the denominator and then Integrate term by term as follows :

Now, you can integrate using the standard integration formulas given below :

For the first part use this formula :

and for the second part, use this formula :

 I assume that you now know what  to use as u and a since we've already discussed enough problems like this.

Answer to 4.1.22 (b) :

For this question, I'll give you two hints and that's enough for you to solve it. Use the two hints :
Hint 1, use the below identity :

and then use this :

And now, with the simplified integrand, you can integrate directly. If you have any doubts, leave it in the comments,

Answer to 4.1.21 (c) :

I'll provide full solution to this question. Anyway, here's the hint 10^x = 2^x * 5^x. The transformation are as follows :

We then split the integrand and integrate both parts separately. See the steps below :

Answer to 4.1.22 (d) :

This is a very simple question and can be done directly. Just remember the fact that sin5a is a constant and it's anti-derivative or integral is xsin5a and NOT -(cos5a)/5 !