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henpen

  • 3 years ago

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

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  1. hartnn
    • 3 years ago
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    know the general formula for 1/(x^2+a^2) ?

  2. henpen
    • 3 years ago
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    trig substitution?

  3. hartnn
    • 3 years ago
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    if, u can't use direct formula.....u can substitute...

  4. henpen
    • 3 years ago
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    What do you mean by general formula?

  5. hartnn
    • 3 years ago
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    \(\\ \huge 16. \int \frac{1}{x^2+a^2}dx=a^{-1}\tan^{-1}(\frac{x}{a})+c \\\)

  6. hartnn
    • 3 years ago
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    first u need to divide by b to be able to use it...

  7. henpen
    • 3 years ago
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    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
    • 3 years ago
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    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
    • 3 years ago
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    *and

  10. henpen
    • 3 years ago
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    OK- I've got that integral- is there any general rule for deciding how to substitute, or is it mainly intuition?

  11. hartnn
    • 3 years ago
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    seen my tutorial, right ? i've given table of substitution there. .

  12. hartnn
    • 3 years ago
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    but yeah, that comes with practice....

  13. henpen
    • 3 years ago
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    Tables are artificial, only useful for engineers. But thanks.

  14. hartnn
    • 3 years ago
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    true... intuition comes with practice....

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