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.

Answered by Aaron T. Maths tutor

2816 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

Amber earns £7 for each hour she works from Monday to Friday. She earns £10 for each hour she works on Saturday. One week Amber worked for 4 hours on Saturday. That week she earned a total of £180. How many hours did Amber work that week?


How do I find the equation of a line connecting points a(p,q) and b(r,s)?


the function f is such that f(x)=(2x-7)/4. Fnd f(-7) and the inverse of the function.


Test


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences