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The value of the integral ∫ e 3 s i n - 1 x 1 1 - x 2 + e 3 c o s - 1 x d x is equal to (where, c is an arbitrary constant)

Options

  1. Ae 3 s i n - 1 x 3 + x e 3 π 2 + c
  2. Be s i n - 1 x + e π / 2 + c
  3. Ce 3 s i n - 1 x 3 + x e 3 π 2 + c
  4. De π 2 + e x π 2 + c

Correct answer

C. e 3 s i n - 1 x 3 + x e 3 π 2 + c

Step-by-step solution

∫ e 3 s i n - 1 x 1 - x 2 d x+ ∫ e 3 s i n - 1 x + c o s - 1 x d x = ∫ e 3 t d t + ∫ e 3 π 2 d x Put   sin - 1 ⁡ x = t = e 3 t 3 + e 3 π 2 ⋅ x + c

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