integration problem no.10
Making the recommended sub, you get:
$\displaystyle 5-(5sin^{2}{\theta}+cos^{2}{\theta})=4cos^{2}{\theta }$
$\displaystyle 5sin^{2}{\theta}+cos^{2}{\theta}-1=4sin^{2}{\theta}$
$\displaystyle \sqrt{\frac{cos^{2}{\theta}}{sin^{2}{\theta}}}=\sq rt{cot^{2}{\theta}}=cot{\theta}$
$\displaystyle \int{cot{\theta}}d{\theta}$
Don't forget to change your limits of integration.