Problem

7) $\int\left(\sec \left(\frac{x}{3}\right) \tan \left(\frac{x}{3}\right)\right) d x$

Answer

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Answer

\boxed{3\sec\left(\frac{x}{3}\right) + C}

Steps

Step 1 ：Substitute u = \(\frac{x}{3}\), then du/dx = \(\frac{1}{3}\), and dx = 3du

Step 2 ：Integrate with respect to u: \(3\int(\sec(u)\tan(u))du = 3\sec(u) + C\)

Step 3 ：Substitute back \(\frac{x}{3}\) for u: \(3\sec\left(\frac{x}{3}\right) + C\)

Step 4 ：\boxed{3\sec\left(\frac{x}{3}\right) + C}

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