Integravimas dalimis

∫xsin3xdx      Kaip išspręsti tokį uždavinį? Dėkui

[tex]\displaystyle \int x\sin (3x)dx[/tex]

Using Integration by parts

taking [tex]x[/tex] as first fun. and [tex]\sin (3x)[/tex] as second function.

[tex] = -x.\frac{\cos (3x)}{3}+\displaystyle \int 1.\frac{\cos 3x}{3}dx[/tex]

[tex] = -x.\frac{\cos (3x)}{3}+\frac{\sin (3x)}{9}+\mathbb{C}[/tex]

So [tex]\displaystyle \int x\sin (3x)dx = --x.\frac{\cos (3x)}{3}+\frac{\sin (3x)}{9}+\mathbb{C}[/tex]