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Provide Solution For R.D.Sharma Maths Class 12 Chapter 18  Indefinite Integrals Exercise  Revision Exercise Question 43 Maths Textbook Solution.

Answers (1)

Answer:

\log \left(\frac{x}{a}+\sqrt{1+\left(\frac{x^{2}}{a^{2}}\right)}\right)+c

Given:

\int \frac{1}{\sqrt{x^{2}+a^{2}}} d x

Hint:

In this statement we assume x as atanθ.

Solution: 

I=\int \frac{1}{\sqrt{x^{2}+a^{2}}} d x                                        \left[\because x=\operatorname{atan} \theta, d x=\operatorname{asec}^{2} \theta d \theta\right]

  I=\int \frac{1}{\sqrt{a^{2} \tan ^{2} \theta+a^{2}}} \operatorname{asec}^{2} \theta d \theta

I=\int \sec \theta d \theta \ldots \ldots \ldots \ldots \ldots \ldots \ldots .\left[1+\tan ^{2} \theta=\sec ^{2} \theta\right]

I=\log |\sec \theta+\tan \theta|+c

I=\log \left(\frac{x}{a}+\sqrt{1+\left(\frac{x^{2}}{a^{2}}\right)}\right)+c

 

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