Question

!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!помогите найти неопределенный интеграл:
1)знак интеграла (3x-2)^2dx
2)знак интеграла (2-x)^4-17x^9+корень из 2)dx

Answer 1

1) I. $int {(3x-2)^2} , dx = int {9x^2-12x+4} , dx = 9int {x^24} , dx - 12int {x} , dx +\+ 4int {} , dx = 9cdot frac{x^3}{3} - 12cdotfrac{x^2}{2} + 4x = 3x^3 - 6x^2 + 4x + C,$
II. $int {(3x-2)^2} , dx = frac{1}{3}int {(3x-2)^2} , d(3x-2) = frac{1}{9}(3x-2)^3+C$

2) $int {(2-x)^4-17x^9+sqrt{2}} , dx = -int {(2-x)^4} , d(2-x) - 17int {x^9} , dx +\+ sqrt{2}int {} , dx = -frac{1}{5}(2-x)^5 - frac{17}{10} x^{10} + x sqrt{2} = 0,2(x-2)^5 - 1,7x^{10} + x sqrt{2}+C$

Answer 2

$1) intlimits {(9x^2-12x+4)} , dx =3x^3-6x^2+4x+C$
$2) intlimits {(16-32x+24x^2-8x^3+x^4-17x^9+ sqrt{2}) } , dx =16x-16x^2+8x^3$$-2x^4+x^5/5-17 x^{10}/10+x sqrt{2} +C$