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 Q8  Integrate the functions x \sqrt { 1+ 2 x^2 }

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Given function  x \sqrt { 1+ 2 x^2 },

\int x \sqrt { 1+ 2 x^2 }\ dx

Assume the 1+2x^2= t

\therefore 4xdx =dt

\Rightarrow \int x\sqrt{1+2x^2}dx = \int \frac{\sqrt {t}}{4} dt

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

= \frac{1}{6}(1+2x^2)^{\frac{3}{2}} +C , where C is any constant value.

Posted by

Divya Prakash Singh

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