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Evaluate : int " sin 5x . cos x dx "...

Evaluate : `int " sin 5x . cos x dx "`

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To evaluate the integral \( \int \sin(5x) \cos(x) \, dx \), we can use the product-to-sum identities. Here’s a step-by-step solution: ### Step 1: Use the Product-to-Sum Identity We know that: \[ \sin(a) \cos(b) = \frac{1}{2} \left( \sin(a + b) + \sin(a - b) \right) \] In our case, let \( a = 5x \) and \( b = x \). Therefore: ...
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