Question

find the integral of x/(x^2+4)dx using trigonometric substitution.

Answer 1

I don't understand why you were instructed to use trig substitution for this question, it is straightforward

You should recognize certain pattern of derivatives and integrals
Notice that the derivative of the denominator is 2x and we have x at the top, so this follows the pattern of log derivatives directly

If we had ∫2x/(x^2 + 4) dx it would simply be ln(x^2 + 4) + c
so for
∫ x/(x^2+4) dx we would get <b> (1/2) ln(x^2 + 4) + c</b>

Answer 2

we are supossed to do it both ways. i got it using the u-substitution method. we are supossed to show that the answers are equivalent.