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  • explain solution RD Sharma class 12 Chapter 18 Indefinite Integrals exercise 18.30 question 5

explain solution RD Sharma class 12 Chapter 18 Indefinite Integrals exercise 18.30 question 5

Answers (1)

Answer:

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

Hint:

            To solve the given integration, first we write the function in simple form and then apply the formula of integration

Given:

            \int \frac{x^{2}+1}{x^{2}-1} d x

Explanation:

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

\begin{aligned} &I=x+2\left(\frac{1}{2} \log \left|\frac{x-1}{x+1}\right|\right)+C \quad\left[\int \frac{1}{x^{2}-a^{2}} d x=\frac{1}{2 a} \log \left|\frac{x-a}{x+a}\right|\right] \\ &I=x+\log \left|\frac{x-1}{x+1}\right|+C \end{aligned}                

 

 

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