Solve ∫ sec^2θ

$$\int \sec ^ { 2 } \theta$$

Evaluate

$$\frac{x}{\left(\cos(\theta )\right)^{2}}+С$$

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

Solution Steps

Find the integral of \frac{1}{\left(\cos(\theta )\right)^{2}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x}{\left(\cos(\theta )\right)^{2}}$$

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

$$\begin{matrix}\frac{x}{\left(\cos(\theta )\right)^{2}}+С_{3},&\end{matrix}$$

Differentiate w.r.t. x

$$\frac{1}{\left(\cos(\theta )\right)^{2}}$$