Question

By using the substitution u = 4 + 3x^2, or otherwise, find

Answer 1

We have the following integral:

`\int (2x)/((4+3x^(2))^(2))dx`

We can use the substitution u= 4 +3x² and we have du= 6x dx, then we have this:

`\int \frac{2x}{(u^{})^2}\cdot(du)/(6x)=(1)/(3)\int u^(-2)du=(1)/(3)\cdot(u^(-1))/(-1)+C=-(1)/(3u)+C=-(1)/(3(4+3x^(2)))+C`