Question

Пожалуйста! Интегралы! Решите хоть что-то!

Answer 1

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