$\int_{0}^{\pi/4} \frac{\sec x}{3\cos x + 4\sin x} dx =$
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For integrals involving trigonometric functions, a common strategy is to divide the numerator and denominator by a power of $\cos x$ or $\sin x$ to convert the expression into terms of $\tan x$ and $\sec^2 x$, which sets up a simple u-substitution.