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.

AT
Answered by Aaron T. Maths tutor

3174 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Make F the subject of the formula: C= 5(F-32) / 9


What is the equation of the tangent of the circle x^2+y^2=25 at the point (3,4)


The point P has coordinates (3, 4) The point Q has coordinates (a, b) A line perpendicular to PQ is given by the equation 3x + 2y = 7 Find an expression for b in terms of a.


Anna and James share out £40 in the ratio 5:3 in that order. How much do they each get?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning