Maths-

General

Easy

Question

# The partial fractions of are

Hint:

### In order to integrate a rational function, it is reduced to a proper rational function. The method in which the integrand is expressed as the sum of simpler rational functions is known as decomposition into **partial fractions**. After splitting the integrand into partial fractions, it is integrated accordingly with the help of traditional integrating techniques.

**The stepwise procedure for finding the partial fraction decomposition is explained here::**

**Step 1: **While decomposing the rational expression into the partial fraction, begin with the proper rational expression.
**Step 2:** Now, factor the denominator of the rational expression into the linear factor or in the form of irreducible quadratic factors (Note: Don’t factor the denominators into the complex numbers).
**Step 3:** Write down the partial fraction for each factor obtained, with the variables in the numerators, say A and B.
**Step 4: **To find the variable values of A and B, multiply the whole equation by the denominator.
**Step 5: **Solve for the variables by substituting zero in the factor variable.
**Step 6:** Finally, substitute the values of A and B in the partial fractions.

**Step 1:**While decomposing the rational expression into the partial fraction, begin with the proper rational expression.**Step 2:**Now, factor the denominator of the rational expression into the linear factor or in the form of irreducible quadratic factors (Note: Don’t factor the denominators into the complex numbers).**Step 3:**Write down the partial fraction for each factor obtained, with the variables in the numerators, say A and B.**Step 4:**To find the variable values of A and B, multiply the whole equation by the denominator.**Step 5:**Solve for the variables by substituting zero in the factor variable.**Step 6:**Finally, substitute the values of A and B in the partial fractions.## The correct answer is:

### Given :

Step 1: While decomposing the rational expression into the partial fraction, begin with the proper rational expression.

Let

Step 2: Write down the partial fraction for each factor obtained, with the variables in the numerators, say A and B.

Step 3: To find the variable values of A and B, multiply the whole equation by the denominator.

On LHS take LCM and cancel the denominators on both side

.

Step 4: Finally, substitute the values of A and B in the partial fractions

=

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