# How do you find the indefinite integral of t^(9/2)+8t^(1/2)-8t^(-1/2)dt?

You can separate it into three integrals and take out $8$ from the integral sign:
$\int {t}^{\frac{9}{2}} \mathrm{dt} + 8 \int {t}^{\frac{1}{2}} \mathrm{dt} - 8 \int {t}^{- \frac{1}{2}} \mathrm{dt} =$
$\int {t}^{n} \mathrm{dt} = {t}^{n + 1} / \left(n + 1\right) + c$
where $n$ is the exponent of $t$