I need explanation. "choose appropriate technique" Integral of 1/(4-t) dt.

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I need explanation. "choose appropriate technique" Integral of 1/(4-t) dt.

Mathematics
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I chose |dw:1439111864731:dw|
the book however chose to just do |dw:1439111938025:dw| How am I suppose to "know" the right formula?
is 4-t similar to a^2 -t^2 or is it similar to a-t ?

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a-t, but there isnt any formula for it in my book. I just do root square.
you can do a substitution, right? plug in u =4-t find du =...
Done, Okey got it. I will have to keep mind all the ways that can be used.
its not always that you'll get a ready form, like integral 1/(2^2-t^2)dt where you can directly use the given formula, sometimes we need to use some formulas or do a substitution to get the integral into the standard form. The thought process for this particular integral is, we have the formula for integral of 1/x dx so just by doing a linear substitution, i can bring it into the form of integral 1/x dx...
with practice, you won't need to find or "keep in mind" all the approaches to solve an integral, they will come to you! :D
I hope so, I have my last exam in calc 2 ever given in 3 weeks.
good luck! :)

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