u=x
dv=sin5xdx
du=dx
v=(1/5)(-cos5x)
=-(x/5)cos5x+(1/5)∫cos5xdx=-(x/5)cos5x+(1/25)sin5x +C;
2) u=arcsinx
du=dx/sqrt(1-x^2)
dv=dx/sqrt(1+x)
v=2sqrt(1+x)
=2(arcsinx)*sqrt(1+x)-2∫sqrt(1+x)dx/sqrt(1-x^2)=
=2(arcsinx)*sqrt(1+x)+2∫d(1-x)/sqrt(1-x)=
=2(arcsinx)*sqrt(1+x)+2*2sqrt(1-x)+C=
=2(arcsinx)*sqrt(1+x)+4sqrt(1-x)+C