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  • Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 5 maths textbook solution

Please solve RD Sharma class 12 chapter Indefinite Integrals exercise 18.26 question 5 maths textbook solution

Answers (1)

Answer:
The correct answer is  \frac{e^{x}}{2 x}+c
 

Given:

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

Solution:

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

On integrating by parts, \int u \cdot v d x=u \int v d x-\int\left[\int v d x \frac{d u}{d x} d x\right]

        \begin{aligned} &=\frac{e^{x}}{2 x}-\int e^{x}\left(\frac{d}{d x}\left(\frac{1}{2 x}\right)\right) d x-\int \frac{e^{x}}{2 x} d x \\ &=\frac{e^{x}}{2 x}+\int \frac{e^{x}}{2 x^{2}} d x-\int \frac{e^{x}}{2 x^{2}} d x \\ &=\frac{e^{x}}{2 x}+c \end{aligned}

So, the correct answer is \frac{e^{x}}{2 x}+c

 

 

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