Integrál (2x-5) cosx dx?

Parcialis integralassal kell.

int(f'g)dx = fg - int(fg')dx

ahol f, g fuggvenyek x-ben

Ha pl f = sinx es g = 2x-5, akkor:

f'g = (cosx)·(2x-5)

fg = (sinx)·(2x-5)

fg' = (sinx)·2

vagyis:

int(2x-5)(cosx)dx = (sinx)(2x-5) - int(2sinx) = (2x-5)sinx + 2cosx + konstans