What is the integral of sec^2(x/4) ?

The integral of sec^2(x/4) is 4tan(x/4)+C

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integral of sec^2(x/4)

\int sec^{2} (\frac{x}{4}) d x

4 tan (\frac{x}{4}) + C

Solution steps

\int sec^{2} (\frac{x}{4}) d x

Apply u-substitution

: \int sec^{2} (u) \cdot 4 d u

= \int sec^{2} (u) \cdot 4 d u

Take the constant out:

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

= 4 \cdot \int sec^{2} (u) d u

Use the common integral:

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

= 4 tan (u)

Substitute back

u = \frac{x}{4}

= 4 tan (\frac{x}{4})

Add a constant to the solution

= 4 tan (\frac{x}{4}) + C

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