# Use integration by parts to find the indefinite integral. (Use

Use integration by parts to find the indefinite integral. (Use C for the constant of integration. Remember to use absolute values where appropriate.)
$\int \frac{0}{8}\mathrm{sec}\left(\frac{0}{8}\right)\mathrm{tan}\left(\frac{0}{8}\right)d0$
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Antum1978
Step 1
In order to evaluate
$\int \frac{0}{8}\mathrm{sec}\left(\frac{0}{8}\right)\mathrm{tan}\left(\frac{0}{8}\right)d0$
Using Integration By Parts Formula
$\int uvd0=u\left(\int vd0\right)-\int \left\{\frac{du}{d0}\int vd0\right\}d0$
Step 2
Considering $u=\frac{0}{8},v=\mathrm{sec}\left(\frac{0}{8}\right)\mathrm{tan}\left(\frac{0}{8}\right)$
$\frac{0}{8}\left(\int \mathrm{sec}\left(\frac{0}{8}\right)\mathrm{tan}\left(\frac{0}{8}\right)d0\right)-\int \left\{\frac{1}{8}\int \mathrm{sec}\left(\frac{0}{8}\right)\mathrm{tan}\left(\frac{0}{8}\right)d0\right\}d0$
$\frac{0}{8}\cdot 8\mathrm{sec}\left(\frac{0}{8}\right)-\int \frac{1}{8}\cdot 8\mathrm{sec}\left(\frac{0}{8}\right)d0$
$0\mathrm{sec}\left(\frac{0}{8}\right)-8\mathrm{ln}|\mathrm{sec}\left(\frac{0}{8}\right)+\mathrm{tan}\left(\frac{0}{8}\right)|+c$