u=x^4+2
du=4x^3dx ⇒ x^3dx=(1/4)du
=(1/4) ∫ du/u=(1/4)ln|u|+C=(1/4)ln |x^4+2|+C=(1/4)ln(x^4+2) + C
б)
u=e^(x)-1
du=e^(x)dx
= ∫ sqrt(u)du= ∫ u^(1/2)du=u^((1/2)+1)/((1/2)+1) + C=
=(2/3)usqrt(u)+C= (2/3)*(e^(x)-1)*sqrt(e^(x)-1) + C
в) по частям
u=x
dv=cos2xdx ⇒ v=(1/2)sin2x
=(1/2)*xsin2x - ∫ (1/2)sin2x dx=
=(1/2)*xsin2x - (1/2)(-cos2x)+C