Answer
\[ = \frac{1}{{10}}\tan \,\left( {10x} \right) + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {{{\sec }^2}10xdx} \hfill \\
\hfill \\
find\,\,du \hfill \\
\hfill \\
u = 10x\,\,\,then\,\,\,du = 10dx\, \hfill \\
\hfill \\
apply\,\,the\,\,\,substitution \hfill \\
\hfill \\
= \frac{1}{{10}}\int_{}^{} {{{\sec }^2}udu} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
= \frac{1}{{10}}\tan u + C \hfill \\
\hfill \\
replace\,\,u\,\,with\,\,\,u = 10x \hfill \\
\hfill \\
= \frac{1}{{10}}\tan \,\left( {10x} \right) + C \hfill \\
\hfill \\
\end{gathered} \]