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Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise 18.18 Question 4 Maths Textbook Solution.

Answers (1)

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

Hint:Let \sin x=t

Given: \int \frac{\cos x}{\sqrt{4+\sin ^{2} x}} d x


                \int \frac{\cos x}{\sqrt{4+\sin ^{2} x}} d x               .......(1)

               let \sin x=t                                         (Differentiate w.r.t to t)

              \cos d x=d t

             From (1) we have

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

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


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