Determine whether each of the following integrals is proper, improper and convergent, or improper and divergent.

? Proper Improper and convergent Improper and divergent   1.   $\displaystyle \int_{5}^{11}\ln(x-5)\,dx$

? Proper Improper and convergent Improper and divergent   2.   $\displaystyle \int_{6}^{\infty}\frac{1}{\sqrt{t^2-36}}\,dt$

? Proper Improper and convergent Improper and divergent   3.   $\displaystyle \int_{-\pi/5}^{11\pi/2}\tan^2(6 x)\,dx$

? Proper Improper and convergent Improper and divergent   4.   $\displaystyle \int_{-6\pi}^{37\pi}\sin(\theta)\arctan(\theta)\,d\theta$

? Proper Improper and convergent Improper and divergent   5.   $\displaystyle \int_{-\infty}^{\infty}\frac{t}{t^2+6}\,dt$

? Proper Improper and convergent Improper and divergent   6.   $\displaystyle \int_{0}^{11}\frac{1}{\sqrt[3]{x-5}}\,dx$

? Proper Improper and convergent Improper and divergent   7.   $\displaystyle \int_{-\infty}^{\infty}\sin(6 z)\,dz$

? Proper Improper and convergent Improper and divergent   8.   $\displaystyle \int_{1}^{\infty}s e^{6 s^2}\,ds$