Question

Решите:

Интеграл(sin^4x+cos^4x)dx

Answer 1

$int{(sin^4 x+cos^4 x)}, dx=\\ int{((sin^2 x+cos^2 x)^2-2sin^2x cos^2 x)}, dx=\\ int{(1-frac {sin^2 (2x)}{2})}, dx=\\ int{(1-frac {frac{1-cos (4x)}{2}}{2})}, dx=\\ int{(1-frac {1-cos (4x)}{4})}, dx=\\ int{(frac{3}{4}+frac {cos (4x)}{4})}, dx=\\ frac{3}{4}x+frac{1}{16}sin(4x)+C$

 

c є R