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## henpen Group Title $\int \frac{ds}{a+bs^2}$ one year ago one year ago

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1. hartnn Group Title

know the general formula for 1/(x^2+a^2) ?

2. henpen Group Title

trig substitution?

3. hartnn Group Title

if, u can't use direct formula.....u can substitute...

4. henpen Group Title

What do you mean by general formula?

5. hartnn Group Title

$$\\ \huge 16. \int \frac{1}{x^2+a^2}dx=a^{-1}\tan^{-1}(\frac{x}{a})+c \\$$

6. hartnn Group Title

first u need to divide by b to be able to use it...

7. henpen Group Title

I've understood that much. What to substitute? A better question: what general logic (other than having seen this problem before, which won't be of help in the future) do I use when deciding what to substitute? It seems with the x^2 the cos^2+sin^2=1 identity may be useful.

8. hartnn Group Title

when there is + ans a square term.. u think of 1+tan^2x = sec^2 x so that u can substitute here s= tan

9. hartnn Group Title

*and

10. henpen Group Title

OK- I've got that integral- is there any general rule for deciding how to substitute, or is it mainly intuition?

11. hartnn Group Title

seen my tutorial, right ? i've given table of substitution there. .

12. hartnn Group Title

but yeah, that comes with practice....

13. henpen Group Title

Tables are artificial, only useful for engineers. But thanks.

14. hartnn Group Title

true... intuition comes with practice....