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henpen
 3 years ago
\[ \int \frac{ds}{a+bs^2} \]
henpen
 3 years ago
\[ \int \frac{ds}{a+bs^2} \]

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hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2know the general formula for 1/(x^2+a^2) ?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2if, u can't use direct formula.....u can substitute...

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0What do you mean by general formula?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2\(\\ \huge 16. \int \frac{1}{x^2+a^2}dx=a^{1}\tan^{1}(\frac{x}{a})+c \\\)

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2first u need to divide by b to be able to use it...

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0I'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
 3 years ago
Best ResponseYou've already chosen the best response.2when there is + ans a square term.. u think of 1+tan^2x = sec^2 x so that u can substitute here s= tan

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0OK I've got that integral is there any general rule for deciding how to substitute, or is it mainly intuition?

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2seen my tutorial, right ? i've given table of substitution there. .

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2but yeah, that comes with practice....

henpen
 3 years ago
Best ResponseYou've already chosen the best response.0Tables are artificial, only useful for engineers. But thanks.

hartnn
 3 years ago
Best ResponseYou've already chosen the best response.2true... intuition comes with practice....
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