Integrate x^2 + 1/ x^3 +3x +2 using limits of 1 and 0

By noticing the the numerator (x^2 + 1) is similar to the derivative of the denominator (x^3 +3x +2) you can integrate the function by using natural logarithms, to form the logarithm ln( x^3 +3x +2). However, the derivative of denominator (x^3 +3x +2) is 3x^2 +3 which is 3 times the size of the numerator (x^2 + 1) meaning an adjustment factor of 1/3 is needed in order to satisfy the integral. This then forms the integral 1/3 ln( x^3 +3x +2) where the limits 1 and 0 can now be substituted into. And, applying these limits results in the equation 1/3ln(6) - 1/3ln(2) which simplfies to 1/3ln(3) due to log laws.