1.
2а-10\3в-9 * 4в-12\а+5= 2(а-5)\3(в-3)* 4(в-3)\а+5=8(а-5)\3(а+5)
(а-1)²\2в : 5а-5\4в= (а-1)(а_10\2в* 4в\5(а-1)=2(а-1)\5
4х\3х-12 - х\х-4=4х\3(х-4)- 12\3(х-4)=4х-12\3(х-4)=4(х-3)\3(х-4)
2.
15в\3-в - 8в\в²-9 * 7в-21\4= 15в\3-в - 8в\(в-3)(в+3)* 7(в-3)\4=15в\3-в - 14в\в+3=15в(в+3)\(3-в)(в+3)-14(3-в)\(3-в)(в+3)=15в²+45-42-14в²\9-в²=в²+3\в²-9
3.
(х\х-у)-ху\х²-у²): 4х²\х²-у²=(х(х+у)\(х-у)(х+у)-ху\(х-у)(х+у)*(х-у)(х+у)\4х²= = х²\(х-у)(х+у)*(х-у)(х+у)\4Х²=1\4
(что-то не получается. 1\4 и все)
A) -4ab-2,5ab-a2 ;
b) 8a2+12a-2,5ab;
c) 5a-4ab-2,5ab
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