Question

Integrate x/(x^2 + 4) dx via trig substitution and by u=x^2+4 substitution. Show that results are equal.

Via trig substitution of x=2 *tan t, I get:
1/2 * tan^-1 (x/2) + c

Via u = (x^2 + 4) substitution, I get:
1/2 * ln |x^2 + 4| + c

How are these equal?

Answer 1

sorry. posted too quickly. got the answer.

Via trig substitution answer comes to:

ln|sqrt(x^2+4)/2| + c

which is the same as the other answer

Answer 2

Yes, good!