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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 59

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Answer: 2 x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+c

Hints: You must know about the integration rules

Given: Write Anti derivative of

 \begin{aligned} &\left(3 \sqrt{x}+\frac{1}{\sqrt{x}}\right) \\ &\int\left(3 \sqrt{x}+\frac{1}{\sqrt{x}}\right) d x \\ &\int 3(x)^{\frac{1}{2}} d x+\int(x)^{\frac{-1}{2}} d x \end{aligned}

\begin{aligned} &\frac{3 x^{\frac{1}{2}+1}}{\frac{1}{2}+1}+\frac{x^{\frac{-1}{2}+1}}{\frac{-1}{2}+1}+c \\ &3 . \frac{2}{3} x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+c \end{aligned}

2 x^{\frac{3}{2}}+2 x^{\frac{1}{2}}+c

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