integral of 1/(4sec(y)) — step-by-step solution

The secant is read as

\sec (u) = \frac{1}{\cos (u)}

, on each interval where

\cos (u) \neq 0

Before performing the integration, let's calculate:

\frac{1}{4 \cdot \frac{1}{\cos (y)}}

\frac{1}{\frac{4}{\cos (y)}}

\frac{\cos (y)}{4}

Let's compute the integral:

\int(\frac{\cos (y)}{4})dy

We attempt to reverse an integration: starting from

\frac{\cos (y)}{4}

and

\frac{d}{d x} (\sin (a)) = \cos (a)

, we differentiate using sin

Let's perform the differentiation:

\frac{d}{d y} (\sin (y))

\cos (y)

The computed derivative matches the original math expression up to a constant factor. Therefore, the integral is:

\frac{1}{4} \cdot \sin (y)

\frac{\sin (y)}{4}

▶Indefinite integrals are defined up to an additive constant C, so this yields:

\frac{\sin (y)}{4} + C