Find the integrals of the function :
${sin}^{2} (2 x + 5)$

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Solution

Let $y = {sin}^{2} (2 x + 5)$

On differentiating both sides with respect to $x$ , we have
$\frac{d y}{d x} = 2 sin (2 x + 5) \times cos (2 x + 5) \times 2$
$\frac{d y}{d x} = 2 \times 2 sin (2 x + 5) cos (2 x + 5)$

We know that $sin 2 A = 2 sin A cos A$

Therefore,
$\frac{d y}{d x} = 2 sin 2 (2 x + 5)$

Hence, this is the answer.

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