Question

Solve this integral (√x-√1-x²)²

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Answer 1

Answer:

here is answer dear friend

Answer 2

Given Integrand,

$\displaystyle \sf \int ( \sqrt{x} - \sqrt{1 - {x}^{2} } ) {}^{2} dx$

Expanding the above expression as (a - b)²,

$\longrightarrow \displaystyle \sf \int \{(\sqrt{x} ) {}^{2} - 2 \sqrt{x(1 - {x}^{2} } ) + (\sqrt{1 - {x}^{2}} ) {}^{2} \} dx \\ \\ \longrightarrow \displaystyle \sf \int \{x - 2 \sqrt{x(1 - {x}^{2} } )+ 1 - {x}^{2} \}dx \\ \\ \longrightarrow \displaystyle \sf \int x dx - 2 \int \sqrt{x(1 - {x}^{2} })dx + \int dx - \int {x}^{2} dx \\ \\ \longrightarrow \displaystyle \sf \dfrac{ {x}^{2} }{2} - 2 \int \sqrt{x(1 - {x}^{2} })dx + x - \dfrac{ {x}^{3} }{3} + c$

The expression can't be integrated further.