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  • explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 20 maths

explain solution RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 20 maths

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Answer:
The correct answer is e^{x} \tan ^{-1} x+c
Hint:

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

Given:

\int e^{x}\left(\tan ^{-1} x+\frac{1}{1+x^{2}}\right) d x

Solution:

        \begin{aligned} &\int e^{x}\left(\tan ^{-1} x+\frac{1}{1+x^{2}}\right) d x \\ &\text { Let } f(x)=\tan ^{-1} x \\ &\text { Then } f^{\prime}(x)=\frac{1}{1+x^{2}} \end{aligned}

        \begin{aligned} &\text { Now, } I=\int e^{x}\left(f(x)+f^{\prime}(x)\right) d x \\ &I=e^{x} f(x)+c \\ &I=e^{x} \tan ^{-1} x+c \end{aligned}

So the correct answer is  e^{x} \tan ^{-1} x+c

 

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