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  • explain solution rd sharma class 12 chapter Indefinite integrals exercise 18.4 question 5 maths

explain solution rd sharma class 12 chapter Indefinite integrals exercise 18.4 question 5 maths

Answers (1)

Answer:

x+\log \left | x+1 \right |+\frac{3}{x+1}+C

Hint:

Use integration by partial fraction.

Given:

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

Solution:

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

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

Put   x+1=t\Rightarrow dx=dt

I=x+\int \frac{t-3}{t^{2}}dt\\ \\ \Rightarrow\hspace{1cm}I=x+\int \frac{1}{t}dt-3\int \frac{1}{t^{2}}dt\\ \\ \Rightarrow\hspace{1cm}I=x+\log\left | t \right |+\frac{3}{t}+c\\ \\ \Rightarrow\hspace{1cm}I=x+\log \left | x+1 \right |+\frac{3}{x+1}+c

 

 

Posted by

infoexpert26

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