What is the integral of sec(a)x ?

The integral of sec(a)x is 1/2 x^2sec(a)+C

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integral of sec(a)x

\int sec (a) x d x

\frac{1}{2} x^{2} sec (a) + C

Solution steps

\int sec (a) x d x

Take the constant out:

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

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

Apply the Power Rule

= sec (a) \frac{x ^{2}}{2}

Simplify

sec (a) \frac{x ^{2}}{2} : \frac{1}{2} x^{2} sec (a)

= \frac{1}{2} x^{2} sec (a)

Add a constant to the solution

= \frac{1}{2} x^{2} sec (a) + C

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