Answer
\[ - \frac{{{\pi ^3}}}{{2{y^2}}} - 2\sqrt {\pi y} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( {\frac{{{\pi ^3}}}{{{y^3}}} - \frac{{\sqrt \pi }}{{\sqrt t }}} \right)} dy \hfill \\
Use\,\,the\,\,sum\,\,and\,\,difference\,\,rules \hfill \\
\int_{}^{} {\frac{{{\pi ^3}}}{{{y^3}}}dy} - \int_{}^{} {\frac{{\sqrt {11} }}{{\sqrt y }}} dy \hfill \\
Write\,\,\frac{1}{{{y^3}}}\,\,as\,\,{y^{ - 3}}\,\,and\,\frac{1}{{\sqrt y }}\,\, = \,\,{y^{ - 1/2}} \hfill \\
\int_{}^{} {{\pi ^3}{y^{ - 3}}dy} - \int_{}^{} {\sqrt \pi {y^{ - 1/2}}dy} \hfill \\
Use\,\,the\,\,power\,\,rule\,\,\int_{}^{} {{y^n}dn} = \frac{{{y^{n + 1}}}}{{n + 1}} + C \hfill \\
{\pi ^3}\,\left( {\frac{{{y^{ - 2}}}}{{ - 2}}} \right) - \sqrt \pi \,\left( {\frac{{{y^{1/2}}}}{{1/2}}} \right) + C \hfill \\
Simplifying \hfill \\
{\pi ^3}\,\left( {\frac{{{y^{ - 2}}}}{{ - 2}}} \right) - \sqrt \pi \,\left( {2{y^{1/2}}} \right) + C \hfill \\
- \frac{{{\pi ^3}}}{{2{y^2}}} - 2\sqrt {\pi y} + C \hfill \\
\hfill \\
\end{gathered} \]
