Решение
1.
b) ∫cos⁵xsinxdx = - ∫cos⁵x d(cosx) = - (cos⁶x) / 6 + C
2.
b) ∫ctg3xdx = ∫[cos(3x)/sin(3x)] * d(x) = (1/3)*∫d(sin(3x)) / sin(3x) =
= (1/3)*lnIsin(3x)I + C
3. ∫sinxdx = - cosx
x = π; x = - π
- [cos(-π) - cosπ] = -[-1 - (-1)] = 0
4. ∫dx/3x = (1/3)*∫dx/x = (1/3)*lnIxI
x = e; x = 1
(1/3)*lne - (1/3)*ln1 = 1/3*1 - (1/3)*0 = 1/3
4а+8б=40
4а=40-8б
а=40/4 - 8б/4
а=10-2б
Z=(-1)²⁵(cos(π/15)+isin(π/15))²⁵=-(cos(25π/15)+isin(25π/15))=-cos(5π/3)-isin(5π/3)=-cos(2π-π/3)-isin(2π-π/3)=-cos(-π/3)-isin(-π/3)=
-cos(π/3)+isin(π/3)=-1/2+i√3/2