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  • provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.26 question 6

provide solution for RD Sharma maths class 12 chapter Indefinite Integrals exercise 18.26 question 6

Answers (1)

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

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

Given:

\int e^{x} \sec x(1+\tan x) d x

Solution:

    I=\int e^{x} \sec x(1+\tan x) d x

        =\int e^{x}(\sec x+\sec x \tan x) d x

Put f(x)=\sec x

     f^{\prime}(x)=\sec x \tan x

                \begin{aligned} &=\int e^{x}(\sec x+\sec x \tan x) d x \\ &=e^{x} \sec x+c \end{aligned}

So, the correct answer is e^{x} \sec x+c.

 

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