Hello everybody my friend and I are doing an exercise but we don't agree on the beginning. Actually we are trying to find the primitive of the function below. So I was wondering if you could take a look at it and give us your point of veiw . Or if you think there is an other way to resolve it please tell me.
$$ A = \int_0^1 \frac{x}{2x+3} \mathrm{d}x $$
The substitution $ t = 2x + 3 \;\implies\; x = (t-3)/2 $, and I found as result $$\ 3/2 \ln (3/5) $$
It can be way done easier. No need for a substitution, this is a bit overkill.
HINT: $$\frac{x}{2x+3}=\frac{1}{2}\frac{2x+3}{2x+3}-\frac{1\frac{1}{2}}{2x+3}$$