Question

Интеграл
∫(5х^4-4х^3+8х^7+2х+3)dx


∫(4^2x•5^3x•1/6^2x)dx

Answer 1

$1); ; int (5x^4-4x^3+8x^7+2x+3)dx=\\=frac{5x^5}{5}-frac{4x^4}{4}+frac{8x^8}{8}+frac{2x^2}{2}+3x+C=x^5-x^4+x^8+x^2+3x+C\\2); ; int frac{4^{2x}+5^{3x}}{6^{2x}}dx=int frac{16^{x}cdot 125^{x}}{36^{x}}dx=int (frac{2000}{36})^{x}dx=int (frac{500}{9})^{x}dx=\\=frac{(frac{500}{9})^{x}}{ln(500/9)}+C= frac{1}{ln500-ln9}cdot (frac{500}{9})^{x}+C$