Resolver ∫ cos2θ/cosθdt

$$\int \frac { \cos 2 \theta } { \cos \theta } d t$$

Ebaluatu

$$\frac{t\cos(2\theta )}{\cos(\theta )}+С$$

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

Ebazpidea

Aurkitu \frac{\cos(2\theta )}{\cos(\theta )}en integrala integral arrunten taulako \int a\mathrm{d}t=at araua erabiliz.

$$\frac{\cos(2\theta )}{\cos(\theta )}t$$

Sinplifikatu.

$$\frac{\cos(2\theta )t}{\cos(\theta )}$$

F\left(t\right) f\left(t\right)ren jatorrizkoa bada, orduan f\left(t\right)ren jatorrizko guztien multzoa ematen du F\left(t\right)+Ck. Beraz, gehitu C\in \mathrm{R} integrazio-konstantea emaitzari.

$$\begin{matrix}\frac{\cos(2\theta )t}{\cos(\theta )}+С_{3},&\end{matrix}$$

Diferentziatu θ balioarekiko

$$t\left(\frac{\cos(2\theta )\tan(\theta )}{\cos(\theta )}-4\sin(\theta )\right)$$