Evalute the integral of x/(x^2+4)dx using u-substitution and then trigonometric substitution. I did this and got (1/2)ln(x^2+4)+C using u-substitution and x^2+4+C using trigonometric substitution. What did I do wrong??? thank you for helping!

Question

Evalute the integral of x/(x^2+4)dx using u-substitution and then trigonometric substitution.  I did this and got (1/2)ln(x^2+4)+C using u-substitution and x^2+4+C using trigonometric substitution.  What did I do wrong???  thank you for helping!

Reiny · Answer

The answer is clearly (1/2) ln(x^2 + 4) + C you can check by taking the derivative I don't know how you got the other answer, but it is definitely incorrect