Integrate:– \Huge{{\large{∫} \frac{dx}{ \sqrt{x √(x) - x {}^(2) } }}}​

Question

Integrate:–
`\Huge{{\large{∫} \frac{dx}{ \sqrt{x √(x) - x {}^(2) } }}}`​

Answer 1

9514 1404 393

Answer:

-4arccos(x^(1/4)) +C

Explanation:

My machine solver gives an answer that reduces to the expression ...

-4arccos(x^(1/4)) +C

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We know that ...

(d/dx)arccos(x) = -1/√(1-x²)

If you let u = x^(1/4), then you can make the integrand look something like ...

4 du/√(1 -u²)

which is what you need to get to the arccos function.