1. definite integrals

$\displaystyle \int_0^{\pi/2} ( sin4 \theta - cos4 \theta)~d\theta$
$\displaystyle \int_1^2(15x^3+e^2x-\frac{4}{x})dx$
2. Well the integral of $\displaystyle sin(4\Theta)$ is $\displaystyle -\frac{1}{4}cos(4\Theta)$
And the integral of $\displaystyle -cos(4\Theta)$ is $\displaystyle -\frac{1}{4}sin(4\Theta)$