Question $1(25$ points$)$

Evaluate the following indefinite integrals.

$(10$ points$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{sin(2x)}{1+co{s}^2(x)}dx$

points${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}t(2t+5{)}^{8}dt$

$(8$ points$){\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{(ln(v^2)+1{)}^4}{v}dv$