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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18 Point 18 Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18 Point 18 Question 2 Maths Textbook Solution.

Answers (1)

Answer:  \log \left|\tan x+\sqrt{4+\tan ^{2} x}\right|+c

Hint: Let

               \tan x=t

Given:   \int \frac{\sec ^{2} x d x}{\sqrt{4+\tan ^{2} x}}

Explanation:   \int \frac{\sec ^{2} x d x}{\sqrt{4+\tan ^{2} x}}

Let    

              \tan x=t

              \sec ^{2} x d x=d t                                                              (Differentiate w.r.t to t)

              =\int \frac{d t}{\sqrt{4+t^{2}}}

              =\int \frac{d t}{\sqrt{(2)^{2}+t^{2}}}

              =\log \left|\mathrm{t}+\sqrt{4+\mathrm{t}^{2}}\right|+c                             \left[\because \int \frac{d x}{\sqrt{x^{2}+a^{2}}}=\log \left|x+\sqrt{x^{2}+a^{2}}\right|+c\right]

            =\log \left|\tan x+\sqrt{4+\tan ^{2} x}\right|+c

 

                

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