Answer
\[\frac{4}{5}{t^{5/4}} + {\pi ^{1/4}}t + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( {{t^{1/4}} + {\pi ^{1/4}}} \right)dt} \hfill \\
Extending\,\,using\,\,the\,\,sum\,\,and \hfill \\
difference\,\,rules \hfill \\
\int_{}^{} {{t^{1/4}}dt + {\pi ^{1/4}}} \int_{}^{} {dt} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\int_{}^{} {{t^n}dt} = \frac{{{t^{n + 1}}}}{{n + 1}} + C \hfill \\
\frac{{{t^{1/4 + 1}}}}{{1/4 + 1}} + {\pi ^{1/4}}t + C \hfill \\
Simplifying \hfill \\
\frac{4}{5}{t^{5/4}} + {\pi ^{1/4}}t + C \hfill \\
\end{gathered} \]
