Question

$$\int_{0}^{8/3}\frac{\cos\ xdx}{(1+\cos\ x)(1-\sin\ x)}.$$

Answer

0

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\imath ntegrate\cos{x}\times 1\times dxfrom\times 0to\times 8}{(1+\cos{x})(1-\sin{x})\times 3}\]
Simplify  \(\imath ntegrate\cos{x}\times 1\times dxfrom\times 0to\times 8\)  to  \(0\).
\[\frac{0}{(1+\cos{x})(1-\sin{x})\times 3}\]
Regroup terms.
\[\frac{0}{3(1+\cos{x})(1-\sin{x})}\]
Simplify.
\[0\]