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

henpen Group TitleBest ResponseYou've already chosen the best response.0
trig substitution?
 2 years ago

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

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

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

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

henpen Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago

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

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

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

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

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

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