(2sin²a+2sinacosa)/(2cos²a+2sinacosa=2sina(sina+cosa)/2cosa(cosa+sina)=
=sina/cosa=tga
1)10sin2x*cos3x=10*1/2(-sinx+sin5x)=5(-sinx+sin5x)
S(10sin2x*cos3x)dx=5S(-sinx+sin5x)dx=5cosx-cos5x+C
2)u=cosx⇒du=sinxdx
Ssinxcos²xdx=Su²du=u³/3=cos³x/3 +C
3)sin²x+3cos²x=1/2(1-cos2x) +3/2(1+cos2x)=1/2(1-cos2x+3+3cos2x)=
=1/2(4+2cos2x)=2+cos2x=1+2cos²x