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

Question

asked Jul 24, 2023 86.0k views

1 Answer

Rkd · Answer 1 · 2023-07-30T14:26:19+0000

Solution

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:

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