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  • please solve rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 10 maths textbook solution

please solve rd sharma class 12 chapter Indefinite Integrals exercise 18.2 question 10 maths textbook solution

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\frac{2}{9} x^{\frac{9}{2}}-4 x^{\frac{1}{2}}+c

Hint: To solve this we multiply\sqrt{x}to next term

Solution:  We have ,  

   I=\int \sqrt{x}(x^{3}-\frac{2}{x})dx

\begin{aligned} &\text { Using identity }\\ &\left\{\int x^{a} d x=\frac{1}{a+1} x^{a+1}+c, a \neq-1\right\}\\ &=\frac{1}{\frac{7}{2}+1} x^{\frac{7}{2}+1}-2 \frac{1}{1-\frac{1}{2}} x^{1-\frac{1}{2}}+c\\ &=\frac{1}{\frac{9}{2}} x^{\frac{9}{2}}-\frac{2}{\frac{1}{2}} x^{\frac{1}{2}}+c\\ &=\frac{2}{9} x^{\frac{9}{2}}-4 x^{\frac{1}{2}}+c \end{aligned}

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