Whakaoti i te ∫ 1/1+tanxdu

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

Aromātai

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

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

Ngā Upane Otinga

Kimihia te tau tōpū o \frac{1}{1+\frac{\sin(x)}{\cos(x)}} mā te whakamahi i te ture mō te ripanga o ngā tau tōpū pātahi \int a\mathrm{d}u=au.

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

Whakarūnātia.

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

Mēnā ko F\left(u\right) he pārōnaki kōaro o f\left(u\right), kāti ko te huinga o ngā pārōnaki kōaro katoa o f\left(u\right) ka whakaaturia e F\left(u\right)+C. Nō reira, me tāpiri te pūmau o te whakatōpūtanga C\in \mathrm{R} ki te otinga.

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

Kimi Pārōnaki e ai ki x

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