What is the integral of sec(2)(x) ?

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

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integral of sec(2)(x)

\int sec (2) (x) d x

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

Solution steps

\int sec (2) x d x

Take the constant out:

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

= sec (2) \cdot \int x d x

Apply the Power Rule

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

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

Simplify

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

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

Add a constant to the solution

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

\frac{d ^{2}}{d x ^{2}} (5 - x^{2})

\frac{5 x - 1}{x + 5}

\frac{\partial}{\partial x} (16 3 x + 2 y)

\int \frac{1}{( x + 1 ) ( 2 x + 1 ) ^{2}} d x

x^{3} - 3 x^{2} - 9 x + 11, at x = 3

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