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  • explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 8 maths

explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 8 maths

Answers (1)

Answer:
The correct answer is e^{x} \log (\sec x+\tan x)+c
Hint:

\int e^{x}\left\{f(x)+f^{\prime}(x)\right\} d x=e^{x} f(x)+c

Given:

: e^{x}[\sec x+\log (\sec x+\tan x)] d x

Solution:

        \begin{aligned} &I=\int e^{x}[\sec x+\log (\sec x+\tan x)] d x \\ &f(x)=\log |\sec x+\tan x| \end{aligned}

        f^{\prime}(x)=\frac{1}{\sec x+\tan x}\left(\sec x \tan x+\sec ^{2} x\right)

                    \begin{aligned} &=\frac{\sec x(\sec x+\tan x)}{\sec x+\tan x} \\ &=\sec x \end{aligned}

                    \begin{aligned} &\int e^{x}\left\{f(x)+f^{\prime}(x)\right\} d x=e^{x} f(x)+c \\ &=e^{x} \log (\sec x+\tan x)+c \end{aligned}

so, the correct answer is  e^{x} \log (\sec x+\tan x)+c

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