can be written as
The numerator can be written as 1/8(8x - 2 - 6)
The first integration is in form of f'(x)/f(x), which is equal to log[f(x)] and second integration can be solved by complting the square in the dinominator.
I must solve using partial fractions:
The only real root for the denominator:
Then
Then I did:
I constructed the system:
Completing the square
Am I on the right way? Its too tedious. The statement says I must use partial fractions, but anyway if you see a simpler way of solving it let me know.
There is no avoiding tedious algebra.
See here: integrate 1/(8x^3 + 1) - Wolfram|Alpha
and click on Show steps.