dx-5-4x-2x-2-

Question Number 86080 by ar247 last updated on 27/Mar/20

\int \frac{d x}{\sqrt{5 - 4 x - 2 x^{2}}}

Commented by ar247 last updated on 27/Mar/20

a n y o n e c a n h e l p m e p l e a s e ?

Answered by Rio Michael last updated on 27/Mar/20

5 - 4 x - 2 x^{2} = (\frac{5}{2} - 2 x - x^{2}) 2

= (\frac{5}{2} - 1 + {(1 - x)}^{2}) 2

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

l e t 1 - x = u \Rightarrow - d u = d x

\int \frac{d x}{\sqrt{5 - 4 x - 2 x^{2}}} = - \frac{1}{2} \int \frac{d u}{\sqrt{\frac{3}{2} + u^{2}}} = - \frac{1}{2} arsinh (\frac{\sqrt{2} x}{\sqrt{3}}) + k

Commented by ar247 last updated on 27/Mar/20

a n y t h i n g e l e s e ?

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