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

2541 Views

See similar Maths GCSE tutors

Related Maths GCSE answers

All answers ▸

A right angled triangle has sides of length 3 and length 4, what is the length of the hypotenuse?


Find the roots of the following equation x^2 + 6x + 5 = 0


The diagram shows a sector ORST of a circle with centre O. OR = OT = 10.4 cm. Angle ROT = 120°. (a) Calculate the length of the arc RST of the sector (3s.f)


Solve the simultaneous equations: (1) x^2 + y^2=41 and (2) y=2x-3


We're here to help

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