Do You Have More Substitution Examples?

In Wednesday’s class, we continued working on the Substitution Method for finding antiderivatives. Below are several more examples.

Example 1 –    \displaystyle \int{\left( 1-t \right){{e}^{2t-{{t}^{2}}}}dt}

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

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

Example 4 –    \displaystyle \int{z\sqrt{{{z}^{2}}-5} dz}

Example 5 –    \displaystyle \int{r\sqrt{{{r}^{2}}+2} dr}

Example 6 –    \displaystyle \int\limits_{0}^{1}{t\frac{1}{3}{{\left( 2z+1 \right)}^{2}}dz}