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Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise18.5 Question 7 Maths Textbook Solution.

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Answer: \frac{2}{3}(x+4)^{\frac{3}{2}}-8(x+4)^{\frac{1}{2}}+C

Hint: Let x+4=t

Given: \int \frac{x}{\sqrt{x+4}}dx


Let x+4=t , x=t+4
\begin{aligned} &d x=d t \\ &=\int \frac{t-4}{\sqrt{t}} d t \\ &=\int \frac{t}{\sqrt{t}} d t-\int \frac{4}{\sqrt{t}} d t \end{aligned}

\begin{aligned} &=\frac{2}{3}(t)^{\frac{3}{2}}-4 \cdot 2(t)^{\frac{1}{2}}+C \\ &=\frac{2}{3}(x+4)^{\frac{3}{2}}-8(x+4)^{\frac{1}{2}}+C \end{aligned}

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