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Please Solve RD Sharma Class 12 Chapter 18 Indefinite Integrals Exercise18.5 Question 3 Maths Textbook Solution.

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Answer: \frac{2}{3}(x+4)^{\frac{3}{2}}-10(x+4)^{\frac{1}{2}}+C

Hint: Use Integration by partial function.

Given: \int \frac{x-1}{\sqrt{x+4}} d x \\


\begin{aligned} &=\int \frac{x-1}{\sqrt{x+4}} d x \\ &=\int \frac{x+4-5}{\sqrt{x+4}} d x \end{aligned}

\begin{aligned} &=\int \frac{x+4}{\sqrt{x+4}} d x-5 \int \frac{d x}{\sqrt{x+4}} \\ &=\int \sqrt{x+4} d x-5 \int(x+4)^{\frac{-1}{2}} \end{aligned}
\begin{aligned} &=\frac{(x+4)^{\frac{1}{2}+1}}{\frac{1}{2}+1}-5 \times \frac{(x+4)^{\frac{-1}{2}+1}}{\frac{-1}{2}+1} \\ &=\frac{2}{3}(x+4)^{\frac{3}{2}}-10(x+4)^{\frac{1}{2}}+C \end{aligned}





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