Réitigh ∫ sec(t)(3sec(t)+7tan(t))

$$\int \sec ( t ) ( 3 \sec ( t ) + 7 \tan ( t ) )$$

Luacháil

$$\frac{x\left(7\sin(t)+3\right)}{\left(\cos(t)\right)^{2}}+С$$

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

Céimeanna Réitigh

Aimsigh suimeálaithe do \frac{3+7\sin(t)}{\cos(t)\cos(t)} ag baint úsáid as an tábla do suimeálaithe coitianta riail\int a\mathrm{d}x=ax.

$$\frac{3+7\sin(t)}{\cos(t)\cos(t)}x$$

Simpligh.

$$\frac{\left(3+7\sin(t)\right)x}{\left(\cos(t)\right)^{2}}$$

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

$$\begin{matrix}\frac{\left(3+7\sin(t)\right)x}{\left(\cos(t)\right)^{2}}+С_{3},&\end{matrix}$$

Difreálaigh w.r.t. x

$$\frac{7\sin(t)+3}{\left(\cos(t)\right)^{2}}$$