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Need Solution for R.D.Sharma Maths Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 15 Maths Textbook Solution.

Answers (1)

Answer:

\frac{\tan ^{7} x}{7}+C

Given:

\int \frac{\sin ^{6} x}{\cos ^{8} x} d x

Hint:

Using  \int x^{n} d x

Explanation:

Let \mathrm{I}=\int \frac{\sin ^{6} x}{\cos ^{8} x} d x

         =\int\left(\frac{\sin ^{6} x}{\cos ^{6} x} \times \frac{1}{\cos ^{2} x}\right) d x

    =\int \tan ^{6} x \sec ^{2} x d x                                                                    \left[\because \tan x=\frac{\sin x}{\cos x} ; \sec x=\frac{1}{\cos x}\right]

              =\int t^{6} d t                                                                          \text { Put } \left.\tan x=t \Rightarrow \sec ^{2} x d x=d t\right]

              \begin{aligned} &=\frac{t^{7}}{7}+C \\ &=\frac{\tan ^{7} x}{7}+C \end{aligned}                                                                  \left[\because \int x^{n} d x=\frac{x^{n+1}}{n+1}+C\right]

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