Answer:
[tex] _{ - \pi} \int ^{\pi} \cos(2(5x) dx = _{ - \pi} \int ^{\pi} \cos(10x) dx \\ let \: 10x \: be \: u \\ \frac{d(10x)}{dx} = du \\ dx = \frac{du}{10} \\ignore \: limits \\ _{ - \pi} \int ^{\pi} \cos(2(5x) dx = \int \cos(u) \frac{du}{10} \\ = \frac{1}{10} \sin(u) + c \\ substitute \: for \: u \\ = \frac{1}{10} \sin(10x) |^{\pi} _{ - \pi} \\ = \frac{1}{10} (( \sin(10\pi) - ( \sin( -10 \pi) ) \\ [/tex]
