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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 37        

Answers (1)

Answer: \frac{x}{2} \sqrt{x^{2}-9}-\frac{9}{2} \log \left|x+\sqrt{x^{2}-9}\right|+c

Given: \int \sqrt{x^{2}-9}dx


\begin{aligned} &\int \sqrt{x^{2}-9} d x \\ &I=\int \sqrt{x^{2}-a^{2}} d x=\int \sqrt{x^{2}-3^{2}} d x \quad\left[\int \sqrt{x^{2}-a^{2}} d x=\frac{x}{2} \sqrt{x^{2}-a^{2}}-\frac{a^{2}}{2} \log \left|x+\sqrt{x^{2}-a^{2}}\right|+c\right] \end{aligned}

Given by

\therefore I=\frac{x}{2} \sqrt{x^{2}-9}-\frac{9}{2} \log \left|x+\sqrt{x^{2}-9}\right|+c

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