Integration - question on trig sub (1 Viewer)

[Giant Lobster]

If you let x = sec@ or something, do u need to specify 0<@<pi/2 or a similar domain for indefinite integrals? And also, after you get ur integral in terms of @, if u try and turn it into terms of x, and there are square roots, do u take the positive or negative root, or both? Its all alright for definite integrals cos you can stick with your set domain for @ but for indefinite im lost

And also, are such trig subs discouraged? I know subbing u=f(x) is faster but its much less versatile and immediately apparent, one would question whether its advantages are worth the time needed to think up a suitable substitution. I guess trig subbing is kinda more safe because it comes with the set of trig rules which add to flexibility, but the bummer at the end is trying to convert back to x for indefinite integrals, which leads be back to my first question about domains n stuff.

 

[KeypadSDM]

Trig subs weren't discouraged when my teacher spoke about them. They're perfectly legitimate ways of solving an integration. the biggest drawback in them is making a simple error in the conversion to and from x. Integration by 'observation' when an integral is in the form:
/
|K * [f(x)]^n * f'(x) dx
/
it's almost always easier to write out what f(x), f'(x) and K are, check they multiply and do the integration:

[K * [f(x)]^(n+1)] /(n+1) + c

Once you get practice at this method, it becomes MUCH quicker than the trig substitutions.

 

[Giant Lobster]

of course, but what if they give you something almost impossible to do normally, such as 1/((1-x)sqrt(1-x^2)). Actually that particular one was meant for subbing u = somethin in x. But I guess not much ppl (well not me at least) are capable of thinking up what to let u be for that one. If it were me id go trig sub for that one and see if it works out.