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(1)/(3+5 cos x)...

`(1)/(3+5 cos x) `

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To solve the integral \(\int \frac{dx}{3 + 5 \cos x}\), we will follow these steps: ### Step 1: Substitute the cosine function We can use the substitution for \(\cos x\) in terms of \(\tan\): \[ \cos x = \frac{1 - \tan^2\left(\frac{x}{2}\right)}{1 + \tan^2\left(\frac{x}{2}\right)} \] Let \(t = \tan\left(\frac{x}{2}\right)\). Then, we have: ...
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