What is the integral of sec^2(x/6) ?

The integral of sec^2(x/6) is 6tan(x/6)+C

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integral of sec^2(x/6)

\int sec^{2} (\frac{x}{6}) d x

6 tan (\frac{x}{6}) + C

Solution steps

\int sec^{2} (\frac{x}{6}) d x

Apply u-substitution

: \int sec^{2} (u) \cdot 6 d u

= \int sec^{2} (u) \cdot 6 d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int sec^{2} (u) d u

Use the common integral:

\int sec^{2} (u) d u = tan (u)

= 6 tan (u)

Substitute back

u = \frac{x}{6}

= 6 tan (\frac{x}{6})

Add a constant to the solution

= 6 tan (\frac{x}{6}) + C

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