Question

Evaluate the integral: ∫x/(x² + 3x + 2) dx

Answer 1

Suppose I = ∫x/(x² + 3x + 2) dx

We can see that there is a term of x in numerator and derivative of x² is also 2x. Therefore there is a chance that we can substitute for x² + 3x + 2 and we can be reduce to a fundamental integration.

Now, we will solve the equation I₁ and I₂ individually.

And we don't have any derivative of function present in denominator. So we will use the some special integrals to solve the problem.

Denominator doesn't have any square root term. Therefore one of the two integral will use to solve the problem.

We have to reduce I₂ such that it matches with any of above two forms.

Then we will make to create a complete square therefore that no individual term of x is seen in denominator.