Calc II integral with quadratic in numerator

[10martineze]

Hi everyone! I need to find the antiderivative(1/(3x^2 + 2)) but am not sure which approach to take. I have tried the following only to arrive at a dead end.

1/3x²+2= .5(1/(3(x/sqrt(2))²+1)= (1/6)(1/((x/sqrt(6))²+(1/3))

Thank you so much!

 

[Mark44]

Hi everyone! I need to find the antiderivative(1/(3x^2 + 2)) but am not sure which approach to take. I have tried the following only to arrive at a dead end.

1/3x²+2= .5(1/(3(x/sqrt(2))²+1)= (1/6)(1/((x/sqrt(6))²+(1/3))

Thank you so much!

Factor a 3 out of the denominator, and then use a trig substitution, which will involve a tangent.
$$\frac{1}{3x^2 + 2} = \frac{1}{3}\frac{1}{x^2 + 2/3}$$