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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) ?
 one year ago

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

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

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

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

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

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

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

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