Question

Помогите пожалуйста с интегралами с 13 по 15

Answer 1

13.∫dx/((x-1)²-9)=∫d(x-1)/((x-1)²-3²)=(1/(2*3))*㏑I(х-1-3)/(х-1+3)I+с=

(1/6)*㏑I(х-4)/(х+2)I+с;

14. ∫dx/(x²-2х+5)= ∫d(x-1)/((x-1)²+1)=arctg(x-1)+c

15. ∫(3x+2)dx/(√(x²-2х+12))

(x²-2x+12)'=2x-2

(3x+2)=(2x-2)*(3/2)+5

x²-2х+12=(x-1)²+11

∫(2x-2)*(3/2)dx/(√(x²-2х+12))+ ∫5dx/(√(x²-2х+12))=

1.5∫d(x²-2х+12)/(√(x²-2х+12))+ 5∫d(x-1)/(√((x-1)²+√11)=

2*1.5*√(x²-2х+12)+5*㏑Ix+1+√x²-2х+12I+c