Solve ∫ sqrt{tanu}

$$\int \sqrt { \tan u }$$

Evaluate

$$x\sqrt{\tan(u)}+С$$

$$\exists n_{1}\in \mathrm{Z}\text{ : }\left(u\geq \pi n_{1}\text{ and }u<\pi n_{1}+\frac{\pi }{2}\right)$$

Solution Steps

Find the integral of \sqrt{\frac{\sin(u)}{\cos(u)}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\sqrt{\frac{\sin(u)}{\cos(u)}}x$$

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.

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

Differentiate w.r.t. x

$$\sqrt{\tan(u)}$$