Question

Интеграл dx/13-9x
интеграл 4cosx/√5
Интеграл dx/(1/3 + 4)^10

Answer 1

$1)\; \; \int \frac{dx}{13-9x}=- \fr \frac{x}{y} ac{1}{9}\cdot ln|13-9x|+C\\\\2)\; \; \int \frac{4cosx}{\sqrt5}dx=\frac{4}{\sqrt5}\int cosx\, dx=-\frac{4}{\sqrt5}sinx+C\\\\3)\int \frac{dx}{(\frac{1}{3}+4)^{10}}=\int \frac{dx}{(\frac{13}{3})^{10}}=(\frac{3}{13})^{-10}\cdot x+C\\\\\\P.S.\; \; \int \frac{dx}{(4/3+4x)^{10}}=\frac{1}{4}\cdot \frac{(4/3+4x)^{-9}}{-9}+C\\\\\int \frac{dx}{(\frac{4}{3}x+4)^{10}}=\frac{3}{4}\cdot \frac{(\frac{4}{3}x+4)^{-9}}{-9}+C$