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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

Answers (1)

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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