całka nieoznaczona tryg.

[zizu_56]

oblicz

\(\displaystyle{ \int xcos \frac{x}{2}dx}\)

[Nakahed90]

Przez części
\(\displaystyle{ u=x}\)
\(\displaystyle{ dv=cos\frac{x}{2}dx}\)

[gufox]

oblicz

\(\displaystyle{ \int_{}^{}}\)\(\displaystyle{ xcos \frac{x}{2}dx}\)

\(\displaystyle{ ...=\begin{cases} u=x,u'=1\\ v'=cos \frac{1}{2}x,v=2sin \frac{1}{2} x \end{cases} =2xsin \frac{1}{2}x-2 \int sin \frac{1}{2}xdx=}\)

\(\displaystyle{ 2xsin \frac{1}{2}x+4cos \frac{1}{2}x+C}\)