1) ((1+lnx)^(3/2))'=3/2(1+lnx)^(1/2)/x
=2/3(1+lnx)^(3/2))
2)
=-1/5инт(2-3cos5x)^(1/3)dcos5x=3/20*(2-3cos5x)^(4/3)*1/3=1/20(2-3cos5x)^(4/3)
4)
x^3+4/(x^2-4x+3)=(x+4)+(13x-8)/(x-1)(x-3)
инт(x+4)dx=x^2/2+4x
A/(x-1)+B/(x-3)=(13x-8)/(x-1)(x-3)
A=-5/2
B=31/2
инт((13x-8)/(x-1)(x-3))dx=1/2[инт(31/(x-3)-5/(x-1))dx]=1/2[31ln|x-3|-5ln|x-1|]
3)
u=arctg2x du=2/(1+4x^2)
dv=xdx v=1/2x^2
x^2*arctg2x/2-1/4инт(x^2/(1/4+x^2))dx=x^2*arctg2x/2-1/4[x-1/2arctg2x]=
=arctg2x[1/8+x^2/2]-x/4