Question

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

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

Answer 2

$1) \int\limits {(9x^2-12x+4)} \, dx =3x^3-6x^2+4x+C$
$2) \int\limits {(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$