Question

решите интегралы S-знак интеграла 1)S xdx/(x^2-20)^(1/2) 2)S dx/(x-1)(x-20) 3)S 3xdx/(x-5)(x-15) 4)S (x-9)dx/(x-1)(x-3) 5)S 16dx/x(x^2-16)

Answer 1

1)=integrate xdx/(sqrt(x^2-20)) [u=x^2-20;du=2xdx]=1/2 integrate du/(sqrt(u))=1/2*(2*sqrt(u))=sqrt(u)=sqrt(x^2-20)+C
2)=-1/(20-1)*ln((x-20)/(x-1))=1/19*(ln(20-x)-ln(1-x))+C
3)=3 integrate xdx/((x-5)(x-15))=-3/2*(ln(5-x)-3*ln(15-x))+C
4)=integrate((4/(x-1))-3/(x-3))dx=4 integrate dx/(x-1)-3 integrate dx/(x-3) [u=x-1;du=dx] =4 integrate du/u-3integrate dx/(x-3)=4*ln(u)-3 integrate dx/(x-3)=4*ln(x-1)-3 integrate dx/(x-3) [u=x-3;du=dx] =4*ln(x-1)-3 integrate du/u=4*ln(x-1)-3*ln(u)=4*ln(x-1)-3*ln(x-3)+C