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  • Provide solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 11

Provide solution for rd sharma maths class 12 chapter Indefinite Integrals exercise 18.2 question 11

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2 x^{\frac{1}{2}}-\frac{1}{2 x^{\frac{1}{2}}}+c

Hint: To solve this equation we use \int x^{n}dx  formula

\text { Given: } \int \frac{1}{\sqrt{x}}\left(1-\frac{1}{x}\right) d x

\begin{aligned} &\text { Solution: } \int \frac{1}{\sqrt{x}}\left(1-\frac{1}{x}\right) d x \\ &=\int x^{\frac{-1}{2}} d x+\int x^{\frac{-3}{2}} d x \quad\left[\int x^{n} d x=\frac{x^{n+1}}{n+1}+c\right] \\ &=2 x^{\frac{1}{2}}-\frac{x^{\frac{-1}{2}}}{\frac{-1}{2}}+c \\ &=2 x^{\frac{1}{2}}-\frac{1}{2 x^{\frac{1}{2}}}+c \end{aligned}

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