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Integrate \int \frac{x+7}{x^{2}(x+2)}dx

  • Option 1)

    5/4ln|x| -7/2x-5/4ln|x+2|+ C

  • Option 2)

    -5/4ln|x| -7/2x-5/4ln|x+2|+ C

  • Option 3)

    -5/4ln|x| -7/2x+5/4ln|x+2|+ C

  • Option 4)

    none of these

Answers (1)

best_answer

As we have learned

Rule for Partial fraction -

Linear and repeated :

\frac{P(x)}{Q(x)}=\frac{P(x)}{(x-a)^{k}(x-a_{1})(x-a_{2})\cdot \cdot \cdot }

\frac{P(x)}{Q(x)}=\frac{A_{1}}{(x-a)}+\frac{A_{2}}{(x-a)^{2}}+\cdot \cdot \cdot \frac{A_{k}}{(x-a)^k}+\frac{A_{k+1}}{(x-a_{1})}+\frac{A_{k+2}}{(x-a_{2})}\cdot \cdot \cdot

- wherein

Where k>1

 

Where find

A_{1} , A_{2} ,A_{3}

by comparing with P(x)

 

 

 \int \frac{(x+7)dx}{x^{2}(x+2)}dx = \int \frac{A}{x}+\frac{B}{x^{2}}+\frac{C}{(x+2)}dx ;on calculating 

A= -5/4 

B= -7/2

C=5/2

\Rightarrow \frac{-5}{4lnx}-7/2x+5/4lx|x+2|+ C

 

 

 


Option 1)

5/4ln|x| -7/2x-5/4ln|x+2|+ C

This is incorrect

Option 2)

-5/4ln|x| -7/2x-5/4ln|x+2|+ C

This is incorrect

Option 3)

-5/4ln|x| -7/2x+5/4ln|x+2|+ C

This is correct

Option 4)

none of these

This is incorrect

Posted by

Aadil

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