I have this integral problem; Is there anyone can help me to solve it?
\begin{align}\label{eq:er8}
ps=\int\limits_{0}^{\infty}\frac{e^{-b~z}}{\sqrt{z}} \Big(\frac{\beta}{\beta+z}\Big)\Big(\frac{\beta+z}{z}\Big)^L e^{\frac{\eta}{z}}\Gamma\left({1-L},\left(\frac{\beta+z}{z}\right)\left(\frac{\delta+z}{\alpha}\right)\right)~dz,
\end{align}
where $\alpha$, $\beta$, $\eta$, $\delta$, and $b$ are real numbers larger than zero. $L=0,1,2,...$
What are the best examples of mathematical induction available at the secondary-school level---totally elementary---that do not involve expressions of the form $\bullet+\cdots\cdots\cdots+\bullet$ where the number of terms depends on $n$ and you're doing induction on $n$?
