Question

integral de ( cos 8x – 2 sen 5x ) dx

Answer 1

$\sf     \int \cos(8x) - 2 \sin(5x) \: dx \\ \\ \\ \sf     \int \cos(8x) \: dx - \int2 \sin(5x) \: dx \\ \\ \\ \sf     \int \frac{ \cos(t) }{8} \: dt - \int2 \sin(5x) \: dx \\ \\ \\ \sf     \frac{1}{8} \cdot \int \cos(t) \: dt - \int2 \sin(5x) \: dx \\ \\ \\ \sf     \frac{1}{8} \cdot \sin(t) - \int2 \sin(5x) \: dx \\ \\ \\ \sf     \frac{1}{8} \cdot \sin(8x) - \int2 \sin(5x ) \: dx \\ \\ \\\sf     \frac{ \sin(8x) }{8} - \int2 \sin(5x) \: dx \\ \\ \\ \sf     \frac{ \sin(8x) }{8} - 2 \cdot \int \sin(5x) \: dx \\ \\ \\ \sf     \frac{ \sin(8x) }{8} - 2 \cdot \int \frac{ \sin(t) }{5} \: dt \\ \\ \\ \sf     \frac{ \sin(8x)}{8} - 2 \cdot \frac{1}{5} \cdot \int \sin(t) \: dt \\ \\ \\ \sf     \frac{ \sin(8x) }{8} - \frac{2}{5} \cdot \int \sin(t) \: dt \\ \\ \\ \sf     \frac{ \sin(8x) }{8} - \frac{2}{5} \cdot( - \cos(t) ) \\ \\ \\ \sf     \frac{ \sin(8x) }{8} - \frac{2}{5} \cdot( - \cos(5x) ) \\ \\ \\ \sf     \frac{ \sin(8x) }{8} + \frac{2 \cos(5x) }{5} \\ \\ \\ {\color{Blue}\boxed{\sf     \frac{ \sin(8x) }{8} + \frac{2 \cos(5x) }{5} + C{,}C\in\mathbb{R}{\color{Lime}\Leftarrow\:Resposta}}}$

Att: Nerd1990