Find: ∫ Sin − 1 ( 2 X ) D X . - Mathematics

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Sum

Find: `int sin^-1 (2x) dx.`

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Solution

`int sin^-1 (2x) dx`

Using ILATE rule

`x sin^-1 2x - int (2x)/sqrt(1-4x^2)dx`

`x sin^-1 2x + 1/4 int (-8x)/sqrt(1-4x^2) dx`

Taking 1 - 4x2 = t

⇒ - 8x dx = dt

`x sin^-1 2x + 1/4 int dt/sqrt(t)`

`x sin^-1 2x + 1/4 (2t 1/2)/1 + "C"`

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

= `x sin^-1 2x + sqrt(1-4x^2)/2 + "C"`

Concept: Integration Using Trigonometric Identities
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