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Q 11 Integrate the functions  \frac{x }{ \sqrt{ x +4} }, x > 0 

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Given function  \frac{x }{ \sqrt{ x +4} },

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

Assume the x+4 =t  so, x =t-4

\therefore dx=dt

\int \frac{x}{\sqrt{x+4}}dx = \int \frac{t-4}{\sqrt{t}}dt

\int t^\frac{1}{2}dt -4\int t^{\frac{-1}{2}}dt

= \frac{2}{3}t^{\frac{3}{2}} - 4\left ( 2t^{\frac{1}{2}} \right )+C

= \frac{2}{3}(x+4)^{\frac{3}{2}} -16(x+4)^{\frac{1}{2}}+C

, where C is any constant value.

Posted by

Divya Prakash Singh

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