вправа 12.32 гдз 11 клас алгебра Істер 2019
Вправа 12.32
Для функції f(x) знайдіть загальний вигляд первісних:
1) f(х) = (8х + 1)7/8; 2) f(х) = 5√4х-13;
3) f(х) = √(4х-1)7; 4) f(х) = 1/(3√6х+3).
1) f(х) = (8х + 1)7/8; 2) f(х) = 5√4х-13;
3) f(х) = √(4х-1)7; 4) f(х) = 1/(3√6х+3).
Умова:
Відповідь ГДЗ:
1) f(х) = (8х + 1)7/8
F(х) = 1/8 • (8х+1)7/8+1/(15/8) =
= 1/8 • (8•(8х+1)15/8)/15
F(х) = (8х+1)15/8/15;
2) f(х) = 5√4х-13
f(х) = (4х - 13)1/5
F(х) = 1/4 • (4х-13)1/5+1/(6/5) =
= 1/4 • (5•(4х-13)6/5)/6 =
= 5/24 • 5√(4х-13)6;
3) f(х) = √(4х-1)7
f(х) = (4х - 1)7/2
F(х) = 1/4 • (4х-1)7/2+1/(9/2) =
= (2•(4х-1)9/2)/(4•9) = (4х-1)9/2/18 =
= 1/18 • √(4х-1)9;
4) f(х) = 1/(3√6х+3)
f(х) = 1/(6х+3)1/3 = (6х + 3)-1/3
F(х) = -1/6 • (6х+3)-1/3+1/2/3 =
= -1/6 • (3•(6х+3)2/3)/2 =
= - (6х+3)2/3/4 = - (3√6х+3)2/4.
F(х) = 1/8 • (8х+1)7/8+1/(15/8) =
= 1/8 • (8•(8х+1)15/8)/15
F(х) = (8х+1)15/8/15;
2) f(х) = 5√4х-13
f(х) = (4х - 13)1/5
F(х) = 1/4 • (4х-13)1/5+1/(6/5) =
= 1/4 • (5•(4х-13)6/5)/6 =
= 5/24 • 5√(4х-13)6;
3) f(х) = √(4х-1)7
f(х) = (4х - 1)7/2
F(х) = 1/4 • (4х-1)7/2+1/(9/2) =
= (2•(4х-1)9/2)/(4•9) = (4х-1)9/2/18 =
= 1/18 • √(4х-1)9;
4) f(х) = 1/(3√6х+3)
f(х) = 1/(6х+3)1/3 = (6х + 3)-1/3
F(х) = -1/6 • (6х+3)-1/3+1/2/3 =
= -1/6 • (3•(6х+3)2/3)/2 =
= - (6х+3)2/3/4 = - (3√6х+3)2/4.