Do You Have Even More Substitution Examples?

The in-person class has spent some time at the board doing substitution problems. I took pictures so that you would have more examples handy. Several of these examples are similar to ones you all have had trouble with on the homework.

There is a lot of good work here…any mistakes? Which solution is easiest to read…and perhaps the best?

Example 1    \displaystyle \int{\left( x+1 \right){{\left( {{x}^{2}}+2x \right)}^{2}}dx}

 

Example 2     \displaystyle \int{4x{{e}^{{{x}^{2}}+9}}dx}

 

Example 3     \displaystyle \int{6x{{e}^{2{{x}^{2}}+1}}dx}

 

Example 4      \displaystyle \int{5x{{e}^{10{{x}^{2}}+4}}dx}

 

Example 5     \displaystyle \int{\frac{\sqrt{2+\ln \left( x \right)}}{x}dx}

 

Example 6     \displaystyle \int{\left( {{x}^{3}}+2x \right){{\left( {{x}^{4}}+4{{x}^{2}}+7 \right)}^{8}}dx}

 

Example 7      \displaystyle \int{\left( 6-6z \right){{e}^{2z-{{z}^{2}}}}dz}

 

Example 8     \displaystyle \int{\left( x+1 \right){{\left( {{x}^{2}}+2x \right)}^{3}}dx}

 

Example 9     \displaystyle \int{\left( 3{{x}^{2}}+4 \right){{\left( 2{{x}^{3}}+8x \right)}^{19}}dx}