Get Answers to all your Questions

header-bg qa

Find  \int \frac{dx}{x^{2}-4}

Option: 1

ln\frac{x+2}{x-2}+ C


Option: 2

1/2ln\frac{x-2}{x+2}+ C


Option: 3

\frac{1}{4}\ln|\frac{x-2}{x+2}|+C


Option: 4

none of these


Answers (1)

best_answer

As we have learned

Rule of integration by Partial fraction -

Linear and non-repeated:

\frac{P(x)}{Q(x)}=\frac{P(x)}{(x-\alpha _{1})(x-\alpha _{2})\cdot \cdot \cdot (x-\alpha _{n})}

Let  \frac{P(x)}{Q(x)}=\frac{A}{(x-\alpha _{1})}+\frac{B}{(x-\alpha _{2})}\cdot \cdot \cdot

Find A,B...

By comparing N^{x} and  P(x) 

-

 

I= \int \frac{dx}{x^{2}-4} = \int \frac{dx}{(x-2)(x+2)}

=-\dfrac{\ln\left(\left|x+2\right|\right)-\ln\left(\left|x-2\right|\right)}{4}+C

=\frac{1}{4}\ln|\frac{x-2}{x+2}|+C 

 

 

 

 

Posted by

Divya Prakash Singh

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions