Solve ∫ wrt y/cosx

$$\int \frac { d y } { \cos x }$$

Evaluate

$$\frac{y}{\cos(x)}+С$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{\pi }{2}$$

Solution Steps

Find the integral of \frac{1}{\cos(x)} using the table of common integrals rule \int a\mathrm{d}y=ay.

$$\frac{y}{\cos(x)}$$

If F\left(y\right) is an antiderivative of f\left(y\right), then the set of all antiderivatives of f\left(y\right) is given by F\left(y\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\begin{matrix}\frac{y}{\cos(x)}+С_{3},&\end{matrix}$$

Differentiate w.r.t. x

$$\frac{y\tan(x)}{\cos(x)}$$