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Need solution for RD Sharma Maths Class 12 Chapter 18 Indefinite Integrals Excercise Very Short Answers Question 54

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Answer: \frac{2 x^{\frac{3}{2}}}{3}-\frac{2 x^{\frac{5}{2}}}{5}+c


Hints: You must know about rules of integration

Given: \int \left ( 1-x \right )\sqrt{x}dx


\begin{aligned} &\int(1-x) \sqrt{x} d x \\ &\int \sqrt{x}-x \sqrt{x} d x \\ &\int x^{\frac{1}{2}}-x^{\frac{3}{2}} d x \\ &\int x^{\frac{1}{2}} d x-\int x^{\frac{3}{2}} d x \end{aligned}
\begin{aligned} &\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}-\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}+c \\ &\frac{2 x^{\frac{3}{2}}}{3}-\frac{2 x^{\frac{5}{2}}}{5}+c\quad\quad\quad\quad\quad\quad\quad\quad\left[\int x^{n} d x=\frac{x^{n+1}}{n+1}\right] \\ \end{aligned}

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