What is the integral of sec(3)(x) ?

The integral of sec(3)(x) is 1/2 sec(3)x^2+C

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integral of sec(3)(x)

\int sec (3) (x) d x

\frac{1}{2} sec (3) x^{2} + C

Solution steps

\int sec (3) x d x

Take the constant out:

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

= sec (3) \cdot \int x d x

Apply the Power Rule

: \frac{x ^{2}}{2}

= sec (3) \frac{x ^{2}}{2}

Simplify

sec (3) \frac{x ^{2}}{2} : \frac{1}{2} sec (3) x^{2}

= \frac{1}{2} sec (3) x^{2}

Add a constant to the solution

= \frac{1}{2} sec (3) x^{2} + C

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What is the integral of sec(3)(x) ?
The integral of sec(3)(x) is 1/2 sec(3)x^2+C