Question

Решите 1,2,6 задания

Answer 1

$1); ; int (5x^9-frac{3}{x}+6, sin2x)dx=5cdot frac{x^{10}}{10}-3cdot ln|x|-6cdot frac{1}{2}cdot cos2x+C\\2); ; int (8x+9), cos6x, dx=[; u=8x+9; ,du=8, dx; ,; ; dv=cos6x, dx; ,\\v=frac{1}{6}, sin6x; ]=uv-int v, du=frac{1}{6}(8x+9)sin, 6x-frac{8}{6}int sin6x, dx=\\=frac{1}{6}(8x+9)sin6x+frac{8}{36}cdot cos6x+C=frac{1}{6}(8x+9)sin6x+frac{2}{9}cdot cos6x+C$

$6); ; int cos^{-6}xcdot sinx, dx=int frac{sinx}{cos^6x}, dx=[; t=cosx; ,; dt=-sinx, dx; ]=\\=-int frac{dt}{t^6}=-int t^{-6}, dt=-frac{t^{-5}}{-5}=frac{1}{5, cos^5x}+C$