∫x1-2x4dx = ______. (where c is a constant of integration) - Mathematics

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MCQ
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`int x/sqrt(1 - 2x^4) dx` = ______.

(where c is a constant of integration)

Options

  • `1/(2sqrt(2)) sin^-1 (2sqrt(2)x^2) + C`

  • `1/2 sin^-1 (2x) + C`

  • `1/sqrt(2) sin^-1 (sqrt(2)x) + C`

  • `1/(2sqrt(2)) sin^-1 (sqrt(2)x^2) + C`

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Solution

`int x/sqrt(1 - 2x^4) dx` = `underlinebb(1/(2sqrt(2)) sin^-1 (sqrt(2)x^2) + C)`.

(where c is a constant of integration)

Explanation:

Let I = `int (x  dx)/sqrt(1 - 2x^4)`

= `int (x  dx)/sqrt(1 - (sqrt(2)x^2)^2`

Let `sqrt(2)x^2` = t

`\implies 2sqrt(2)x  dx` = dt

`\implies` x dx = `dt/(2sqrt(2))`

∴ I = `1/(2sqrt(2)) int dt/sqrt(1 - t^2)`

= `1/(2sqrt(2)) sin^-1 (t) + C`

I = `1/(2sqrt(2)) sin^-1 (sqrt(2)x^2) + C`

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