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  • Explain Solution R.D Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise Question 28 Maths Textbook Solution.

Explain Solution R.D Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Revision Exercise  Question 28 Maths Textbook Solution.

Answers (1)

Answer:

\frac{1}{2} \tan ^{2} x-\log |\sec x|+c

Given:

\int \tan ^{3} x d x

Hint:

To solve this statement we have to change tan into sec form.

Solution: 

\int \tan ^{2} x \cdot \tan x d x

   \int\left(\sec ^{2} x-1\right) \tan x d x \quad\left(\tan ^{2} x=\sec ^{2} x-1\right)

\int \sec ^{2} x \tan x d x-\int \tan x d x

                                                

I_{1}=\int \sec ^{2} x \tan x d x                                                        \left[\because \tan x=t, \sec ^{2} x d x=d t, \int x^{n} d x=\frac{x^{n+1}}{n+1}\right]

I_{1}=\int t d t

       =\frac{t^{2}}{2}=\frac{1}{2} \tan ^{2} x

I=I_{1}+I_{2}

    =\frac{1}{2} \tan ^{2} x-\log |\sec x|+c

 

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