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

The integral of sec^2(x/pi) is pitan(x/pi)+C

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integral of sec^2(x/pi)

\int sec^{2} (\frac{x}{π}) d x

π tan (\frac{x}{π}) + C

Solution steps

\int sec^{2} (\frac{x}{π}) d x

Apply u-substitution

= \int sec^{2} (u) π d u

Take the constant out:

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

= π \cdot \int sec^{2} (u) d u

Use the common integral:

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

= π tan (u)

Substitute back

u = \frac{x}{π}

= π tan (\frac{x}{π})

Add a constant to the solution

= π tan (\frac{x}{π}) + C

What is the integral of sec^2(x/pi) ?
The integral of sec^2(x/pi) is pitan(x/pi)+C