henpen 2 years ago $\int \frac{ds}{a+bs^2}$

1. hartnn

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

2. henpen

trig substitution?

3. hartnn

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

4. henpen

What do you mean by general formula?

5. hartnn

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

6. hartnn

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

7. henpen

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

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

*and

10. henpen

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

11. hartnn

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

12. hartnn

but yeah, that comes with practice....

13. henpen

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

14. hartnn

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