How do you differentiate $\frac{cos (x)}{2 + sin (x)}$ $( cos (x) ) / ( 2 + sin (x) )$ ?

Question

1456 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-21T07:14:49

$\int \frac{cos x}{2 + sin x} d x = ln (2 + sin x) + c$ $intcosx/(2+sinx)dx=ln(2+sinx)+c$

Let $u = 2 + sin x$ $u=2+sinx$ , then $d u = cos x d x$ $du=cosxdx$ and

$\int \frac{cos x}{2 + sin x} d x$ $intcosx/(2+sinx)dx$

= $\int \frac{d u}{u}$ $int(du)/u$

= $ln u + c$ $lnu+c$

= $ln (2 + sin x) + c$ $ln(2+sinx)+c$

How do you differentiate cos(x)2+sin(x) ( cos (x) ) / ( 2 + sin (x) )?