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  • please solve rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 6 maths textbook solution

please solve rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 6 maths textbook solution

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\frac{x^{3}}{2}+\log x-2 x+c

Hint: To solve this equation we use (a-b)^{2} formula then \int x^{a}dx

\begin{aligned} &\text { Given: } \int\left[\sqrt{x}-\frac{1}{\sqrt{x}}\right]^{2} d x \\ &\text { Solution: } \int\left[(\sqrt{x})^{2}-2 \sqrt{x} \frac{1}{\sqrt{x}}-\left(\frac{1}{\sqrt{x}}\right)^{2}\right] d x \quad\left\{(a-b)^{2}=a^{2}-b^{2}+2 a b\right\} \end{aligned}

\\ \\ \Rightarrow \hspace{1cm}I=\int (x-2+\frac{1}{x})dx\\ \\ \Rightarrow \hspace{1cm}I=\frac{x^{2}}{2}-2x+\log \left | x \right |+c.

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