1. ∫(eˣ-1/x)dx=eˣ-ln|x|+c
2. ∫(sinx+4cosx-5√x)dx=-cosx+4sinx-5*3√x*x/2=-cosx+4sinx-7.5x√x+c
3. ∫(6-3x)⁷dx 6-3x=z 3x=6-z x=2-z/3 dx=-dz/3
∫(6-3x)⁷dx=-1/3∫z⁷dz=-1/3*8*z⁸=z⁸/24=(6-3x)⁸/24
<span>(33 - x)*(16 + 2x) < 0
</span><span>(33 - x)*(16 + 2x) = 0 корни 33 и -8
----------- (-8) ++++++++ (33)--------------------
x=(-00 -8) U (33 +00)</span>
1)8cosπ/33*cos2π/33*cos4π/33*cos8π/33*
cos16π/33=(умножим делим sinπ/33)=
(8*cosπ/33*sinπ/33):(sinπ/33)*(cos2π/33*
cos4π/33)*cos8π/33*cos16π/33=
=4/(sinπ/33)*sin2π/33*cos2π/33*cos4π/33*
cos8π/33*cos16π/33=2/(sinπ/33)*sin4π/33*
cos4π/33*cos8π/33*cos16π/33=1/(sin2π/33)*
sin8π/33*cos8π/33*cos16π/33=1/(sinπ/33)*1/2*
sin16π/33*cos16π/33
1/(sinπ/33)*1/2*1/2sin32π/33=1/(sinπ/33)*1/4*
sin(π-32π/33)=1/(sinπ/33)*
1/4*sinπ/33=1/4
(2 - x)² - (3x + 5)² = (2 - x + 3x + 5)(2 - x - 3x - 5) =
=(2x + 7)(-4x - 3) = -(2x + 7)(4x + 3)
В 5)
15x^2 - 3 = 3*5*x^2 - 3*1
Тройка - общий множитель