Issolvi ∫ cscθcotθ

$$\int \csc \theta \cot \theta$$

Evalwa

$$\frac{x\cot(\theta )}{\sin(\theta )}+С$$

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

Passi tas-Soluzzjonijiet

Sib l-integru ta' \frac{\cos(\theta )}{\left(\sin(\theta )\right)^{2}} billi tuża t-tabella tar-regola tal-integrali komuni \int a\mathrm{d}x=ax.

$$\frac{\cos(\theta )}{\left(\sin(\theta )\right)^{2}}x$$

Issimplifika.

$$\frac{\cos(\theta )x}{\left(\sin(\theta )\right)^{2}}$$

Jekk F\left(x\right) huwa antiderivattiv ta' f\left(x\right), allura s-sett tal-antiderivati kollha ta' f\left(x\right) jingħata minn F\left(x\right)+C. Għalhekk, żid il-kostanti ta' integrazzjoni C\in \mathrm{R} mar-riżultat.

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

Iddifferenzja w.r.t. x

$$\frac{\cot(\theta )}{\sin(\theta )}$$