see the derivative of denominator is 3x^2 + 3 = 3(x^2+1) Thus you can write
(x^2+1) / ( x^3 + 3x + 7 ) = 1/3 [ 3(x^2+1) + 7] /( x^3 + 3x + 7 )
But still I observe that you will have a problem integrating 7 / ( x^3 + 3x + 7 )
So we are having a holiday right now and I decide to go over the math which I'm bad at "partial fraction"
The question is my exercise book is
so I work around with the algebra a bit and got the equation to become
the problem is that I wasn't sure how to integrate this since I cannot factorise the denominator into somethign like (x^2+A)(x+B)
so how does one set up for partial fractions
Best Regards
Junks
see the derivative of denominator is 3x^2 + 3 = 3(x^2+1) Thus you can write
(x^2+1) / ( x^3 + 3x + 7 ) = 1/3 [ 3(x^2+1) + 7] /( x^3 + 3x + 7 )
But still I observe that you will have a problem integrating 7 / ( x^3 + 3x + 7 )