Réitigh ∫ 1/1+tanxdu

$$\int \frac { 1 } { 1 + \tan x } d u$$

Luacháil

$$\frac{u\cos(x)}{\sin(x)+\cos(x)}+С$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}+\frac{3\pi }{4}$$

Céimeanna Réitigh

Aimsigh suimeálaithe do \frac{1}{1+\frac{\sin(x)}{\cos(x)}} ag baint úsáid as an tábla do suimeálaithe coitianta riail\int a\mathrm{d}u=au.

$$\frac{u}{1+\frac{\sin(x)}{\cos(x)}}$$

Simpligh.

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

Má tá F\left(u\right) mar frithdhíorthach do f\left(u\right), beidh tacar do frithdhíorthach uile do f\left(u\right) a thabhairt ag F\left(u\right)+C. Mar sin de, cur an comhtháthú leanúnach C\in \mathrm{R} don toradh.

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

Difreálaigh w.r.t. x

$$-\frac{u}{\left(\sin(x)+\cos(x)\right)^{2}}$$