anonymous
  • anonymous
\[ \int \frac{ds}{a+bs^2} \]
Mathematics
schrodinger
  • schrodinger
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hartnn
  • hartnn
know the general formula for 1/(x^2+a^2) ?
anonymous
  • anonymous
trig substitution?
hartnn
  • hartnn
if, u can't use direct formula.....u can substitute...

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

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