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 Q 7  Integrate the functions  x \sqrt { x +2 }

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Given function x \sqrt { x +2 },

\int x\sqrt{x+2}

Assume the (x+2) = t19634

\therefore dx =dt

\Rightarrow \int x\sqrt{x+2} dx = \int (t-2) \sqrt{t} dt

= \int (t-2) \sqrt{t} dt

= \int \left ( t^{\frac{3}{2}}-2t^{\frac{1}{2}} \right )dt

= \int t^{\frac{3}{2}}dt -2\int t^{\frac{1}{2}}dt

= \frac{t^{\frac{5}{2}}}{\frac{5}{2}} -2\left ( \frac{t^{\frac{3}{2}}}{\frac{3}{2}} \right ) +C

= \frac{2}{5}t^{\frac{5}{2}} -\frac{4}{3}t^{\frac{3}{2}} +C

Back substituting the value of t in the above equation.

or, \frac{2}{5}(x+2)^{\frac{5}{2}}- \frac{4}{3}(x+2)^\frac{3}{2} +C , where C is any constant value.

 

Posted by

Divya Prakash Singh

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