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  • Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 3 Maths Textbook Solution.

Please Solve R.D.Sharma Class 12 Chapter 18 Indefinite Integrals Exercise Multiple Choice Questions Question 3 Maths Textbook Solution.

Answers (1)

Answer:

\frac{1}{2} \log \left(\sec x^{2}+\tan x^{2}\right)+C

Given:

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

Hint:

Using \int \sec \theta d \theta

Explanation:

Let,\mathrm{I}=\int x \sec x^{2} d x                                            \left[\text { Put } x^{2}=t \Rightarrow 2 x d x=d t \Rightarrow x d x=\frac{d t}{2}\right]

         \begin{aligned} &=\int \sec t \cdot \frac{d t}{2} \\ &=\frac{1}{2} \int \sec t d t \\ &=\frac{1}{2} \log |\sec t+\tan t|+C \end{aligned}                    \left\{\int \sec x d x=\log |\sec x+\tan x|+c\right\}

         =\frac{1}{2} \log \left|\sec x^{2}+\tan x^{2}\right|+C

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