Question

Интеграл
∫(5х^4-4х^3+8х^7+2х+3)dx


∫(4^2x•5^3x•1/6^2x)dx

Answer 1

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