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3x³ /3 + 4x⁶/(6x3) = x³ + 2x⁶/9 + c

4(x+13)

Firstly, ensure both numerator and denominator are factorised fully so that any possible cancellations can happen - making it easy for yourself is always a good idea. Now, turn it into partial fractions. ...

To factorise we must think what two numbers add up to 5 but times together to get 6. We know it is two numbers because it is x^(2). If it was x^(3) there could be 3 numbers, ect. We think what goes into 6...

Firstly we notice that the numerator is the derivative of the denominator so we can use integration by subsitution method. Setting u=x^(2)+1. We can differentiate this to get du/dx=2x Subbing in dx=du/2x ...