\[ \int \frac{ds}{a+bs^2} \]

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\[ \int \frac{ds}{a+bs^2} \]

Mathematics
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know the general formula for 1/(x^2+a^2) ?
trig substitution?
if, u can't use direct formula.....u can substitute...

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What do you mean by general formula?
\(\\ \huge 16. \int \frac{1}{x^2+a^2}dx=a^{-1}\tan^{-1}(\frac{x}{a})+c \\\)
first u need to divide by b to be able to use it...
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.
when there is + ans a square term.. u think of 1+tan^2x = sec^2 x so that u can substitute here s= tan
*and
OK- I've got that integral- is there any general rule for deciding how to substitute, or is it mainly intuition?
seen my tutorial, right ? i've given table of substitution there. .
but yeah, that comes with practice....
Tables are artificial, only useful for engineers. But thanks.
true... intuition comes with practice....

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