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  • need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.4 question 4

need solution for rd sharma maths class 12 chapter Indefinite integrals exercise 18.4 question 4

Answers (1)

Answer:

2\log \left | x-1 \right |-\frac{5}{x-1}+C

Hint:

Use integration by partial fraction.

Given:

\int \frac{2x+3}{\left ( x-1 \right )^{2}}dx

Solution:

\frac{2x+3}{\left ( x-1 \right )^{2}}

=\frac{2x-2+2+3}{\left ( x-1 \right )^{2}}

=\frac{2\left ( x-1 \right )+5}{\left ( x-1 \right )^{2}}

=\frac{2}{\left ( x-1 \right )}+\frac{5}{\left ( x-1 \right )^{2}}

I=\int \frac{2}{x-1}dx+\int \frac{5}{(x-1)^{2}}dx                                  

 

\left [ \int \frac{1}{x}dx= \log \left | x \right |+C \right ]=2

I= \log \left | x-1 \right |-\frac{5}{x-1}+C                                                

 

Posted by

infoexpert26

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