Calc II integral with quadratic in numerator

  • #1
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!
 

Answers and Replies

  • #2
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5,794
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.
[tex]\frac{1}{3x^2 + 2} = \frac{1}{3}\frac{1}{x^2 + 2/3}[/tex]
 

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