# Evaluate the following integral:

Let substitute, so the given equation becomes

Factorizing the denominator, we get

The denominator is factorized, so let separate the fraction through partial fraction, hence let

1 = A(3u + 2) + B(2u + 1)……(ii)

We need to solve for A and B. One way to do this is to pick values for x which will cancel each variable.

Put in the above equation, we get

Now put in equation (ii), we get

We put the values of A and B values back into our partial fractions in equation (ii) and replace this as the integrand. We get

Split up the integral,

Let substitute

z = 2u + 1 dz = 2du and y = 3u + 2 dy = 3du so the above equation becomes,

On integrating we get

Substituting back the value of z, we get

Now substitute back the value of u, we get

Applying the rules of logarithm we get

Note: the absolute value signs account for the domain of the natural log function (x>0).

Hence,

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Fundamental Integration Formula59 mins
Interactive Quiz on Integration by Substitution47 mins
Lecture on Integration by parts55 mins
Lecture on some forms of integration54 mins
Lecture on integration by partial fractions62 mins
Interactive Quiz on Integration by Parts56 mins
Integration by Substitution56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Evaluate the following:

Mathematics - Exemplar

If log |x + 2| + C, then

Mathematics - Exemplar

Find :

Mathematics - Board Papers