Question

Помогите решить примеры​

Answer 1

Ответ:

$1)\ \ \int \Big(x^5-6x^4+3x-8\Big)\, dx=\dfrac{x^6}6}-6\cdot \dfrac{x^5}{5}+3\cdot \dfrac{x^2}{2}-8x+C=\\\\\\=\dfrac{x^6}{6}-\dfrac{6x^5}{5}+\dfrac{3x^2}{2}-8x+C\ \;\\\\\\2)\ \ \int 6\cdot \Big(x^8-\dfrac{1}{2}\, x^7+2x^3-6\Big)\, dx=6\cdot \Big(\dfrac{x^9}{9}-\dfrac{1}{2}\cdot \dfrac{x^8}{8}+2\cdot \dfrac{x^4}{4}-6x\Big)+C=\\\\\\=\dfrac{2x^9}{3}-\dfrac{3x^8}{8}+3x^4-36x+C$

$3)\ \ \int 7\cdot \Big(\dfrac{3}{4}\, x^5-\dfrac{2}{7}\, x^4+6x^3-4x+5\Big)\, dx=\\\\\\=7\cdot \Big(\ \dfrac{3}{4}\cdot \dfrac{x^6}{6}-\dfrac{2}{7}\cdot \dfrac{x^5}{5}+6\cdot \dfrac{x^4}{4}-4\cdot \dfrac{x^2}{2}+5x\ \Big)+C=\\\\\\=\dfrac{7x^6}{8}-\dfrac{2x^5}{5}+\dfrac{21x^4}{2}-14x^2+35x+C$