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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise 18.15 Question 6

Answers (1)

Answer:

            \log \left|\frac{(x+3)^{2}}{(x+2)}\right|+C

Hint:

            To solve this problem use special integration formula

Given:

            \int \frac{(x+1)}{(x+2)(x+3)} d x

Solution:

Let   I=\int \frac{(x+1)}{(x+2)(x+3)} d x

Applying partial fraction   

\begin{aligned} &\frac{(x+1)}{(x+2)(x+3)}=\frac{A}{(x+2)}+\frac{B}{(x+3)} \\ & \end{aligned}

(x+1)=A(x+3)+B(x+2)

Putting 

\begin{aligned} &x=-2 \\ \end{aligned}

(-2+1)=A(-2+3)+B(-2+2) \\

A=-1

Putting

\begin{aligned} &x=-3 \\ \end{aligned}

(-3+1)=A(-3+3)+B(-3+2) \\

-2=0+B(-1) \\

B=2

\begin{aligned} &I=\int \frac{x+1}{(x+1)(x+2)} d x=\int \frac{-1}{x+2} d x+\int \frac{2}{x+3} d x \\ \end{aligned}

=-\log |x+2|+2 \log |x+3| \\

=\log \left|\frac{(x+3)^{2}}{(x+2)}\right|+C

 

 

Posted by

infoexpert27

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