Пошаговое объяснение:
1)
∫(12x²+6x-8)dx = 12∫x²dx +6∫xdx -8∫dx = 12*(x³/3)+6*(x²/2) -8x+C=
=4x³ + 3x² - 8x + C
2)
∫(7/x -4sinx +2eˣ)dx = ∫(7/x)dx -4∫(sinx)dx +2∫(eˣ)dx = 7lnx -4(-cosx) +2eˣ+C=
= 7lnx + 4cosx + 2eˣ + C
3)
∫(1/√x - 3/x⁴ + 3)dx = ∫(1/√x)dx - 3∫(1/x⁴)dx + 3∫(x)dx =2√x +5/3x³ +3x +C
4)
![\displaystyle \int {(3x-5)^8} \, dx =\left[\begin{array}{ccc}u = 3x-5\\du = 3dx \hfill\\\end{array}\right] = \frac{1}{3} \int{u^8} \, du=\frac{1}{3} *\frac{u^9}{9} +C = \frac{(3x-5)^9}{27} +C](/tpl/images/1699/6255/42442.png)
