Simple linear factors

Evaluate the following integrals.

Problem 10E

Step 1</p>

In this problem we have to evaluate

Let us solve this by using Partial Fractions.

Let us first see about Partial Fractions.

When a proper rational expression is decomposed into a sum of two or more rational expressions, it is known as Partial Fractions.

Consider … (1)

Taking LCM in the right hand side we get,

Since the denominators of both sides are same, we can equate the numerator.

Put we get

Put we get

Step 2</p>

Thus (1) becomes,

Thus

… (2)

Take

Differentiating we get

Thus (2) becomes

.. (3)