The discussion centers on finding the antiderivative of the function 1/(3x² + 2). A participant suggests factoring out a 3 from the denominator and applying a trigonometric substitution involving tangent. The transformation leads to the expression 1/3 * 1/(x² + 2/3), which simplifies the integration process. This method provides a clear pathway to solving the integral effectively.
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Factor a 3 out of the denominator, and then use a trig substitution, which will involve a tangent.10martineze said: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!