∫dx/(x-2)²(x-3)=∫dx/(x-2)(x-3)-∫dx/(x-2)²=∫dx/(x-3)-∫dx/(x-2)-∫dx/(x-2)²=ln│x-3│-ln│x-2│+1/(x-2)+C
=ln│(x-3)/(x-2)│+1/(x-2)+C
∫sinxsin2xsin3xdx=∫sinx·2sinxcosx·(3sinx-4sin³x)dx=∫[6sin³x-8(sinx)^5]dsinx
=3/2(sinx)^4-4/s(sinx)^6+C
∫(x²-5x+9)dx/(x²-5x+6)=∫1dx+3∫dx/(x-2)(x-3)=x+3∫dx/(x-3)-3∫dx/(x-2)=x+3ln│(x-3)/(x-2)│+C
∫cosxdx/sinx(1+sinx)²=∫dsinx[1/sinx(1+sinx)-1/(1+sinx)²]=∫dsinx[1/sinx-1/(1+sinx)-1/(1+sinx)²]
=ln│sinx/(1+sinx)│+1/(1+sinx)+C
∫x²dx/(x²+1)=∫dx-∫dx/(x²+1)=x-arctanx+C