Question

Найдите общий вид первообразных F(x) для функции
$f(x) = \frac{1}{4} \sin( \frac{x}{4} ) + \frac{1}{5} \cos( \frac{x}{5} )$
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Answer 1

$\sin(\frac{x}{5})'=\frac{1*x^0}{5}\cos(\frac{x}{5})=\frac{1}{5}\cos(\frac{x}{5})$

$f(x) =\frac{1}{4}\sin(\frac{x}{4})+\frac{1}{5}\cos(\frac{x}{5})\\F(x)=-\frac{4}{4}\cos(\frac{x}{4})+\frac{5}{5}\sin(\frac{x}{5})+c\\F(x)=\sin(\frac{x}{5})-\cos(\frac{x}{4})+c$