The integral 1 + 2 x ( cosec x + x ) ,dx, (0 < x < 2 ) is equal to:

JEE Main 2017 Mathematics question

The integral , is equal to:

Answer: (1)

Simplify the radicand. Expanding,

1 + 2 x\operatorname{cosec}x + 2x = (1 + x) + x + 2 x\operatorname{cosec}x = \operatorname{cosec}^2x + x + 2\operatorname{cosec}x x,

using . This is a perfect square:

= (\operatorname{cosec}x +

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Question ID VK-115845