Answers: 2
![u = [sec(u)]^{n-2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ dv = sec^2(u)du\\du = (n-2)[sec(u)]^{n-3} sec(u)tan(u) \ \ \ \ \ \ \ \ v = tan(u)](/tpl/images/0993/4015/3c1e4.png)
![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - \int [{tan(u)(n-2)[sec(u)]^{n-3}sec(u)tan(u)} ]\, du](/tpl/images/0993/4015/87ad0.png)
[Integral - Alg] Multiply: ![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - \int [{tan^2(u)(n-2)[sec(u)]^{n-2}}] \, du](/tpl/images/0993/4015/6caa7.png)
[integral - Int Rule 1] Simplify: ![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - (n-2)\int [{tan^2(u)[sec(u)]^{n-2}}] \, du](/tpl/images/0993/4015/e7ab9.png)
[Integral - Pythagorean Identities] Rewrite: ![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - (n-2)\int [{[sec^2(u) - 1][sec(u)]^{n-2}}] \, du](/tpl/images/0993/4015/95839.png)
[Integral - Alg] Multiply/Distribute: ![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - (n-2)\int [{sec^n(u)-[sec(u)]^{n-2}}] \, du](/tpl/images/0993/4015/9dc33.png)
[Integral - Int Rule 2] Rewrite: ![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - (n-2) [\int {sec^n(u)} \, du - \int {[sec(u)]^{n-2}} \, du ]](/tpl/images/0993/4015/35f92.png)
[Integral - Alg] Distribute: ![\int {sec^n(u)} \, du = tan(u)[sec(u)]^{n-2} - (n-2) \int {sec^n(u)} \, du + (n-2)\int {[sec(u)]^{n-2}} \, du](/tpl/images/0993/4015/337ad.png)
Rewrite: ![\int {sec^n(u)} \, du = sec^{n-2}(u)tan(u) - (n-2) \int {sec^n(u)} \, du + (n-2)\int {[sec(u)]^{n-2}} \, du](/tpl/images/0993/4015/84094.png)
[Integral - Alg] Isolate Integral Term: ![\int {sec^n(u)} \, du + (n-2) \int {sec^n(u)} \, du = sec^{n-2}(u)tan(u) + (n-2)\int {[sec(u)]^{n-2}} \, du](/tpl/images/0993/4015/7c04a.png)
[Integral - Alg] Combine Like Terms: ![(n - 1)\int {sec^n(u)} \, du = sec^{n-2}(u)tan(u) + (n-2)\int {[sec(u)]^{n-2}} \, du](/tpl/images/0993/4015/9805a.png)
[Integral 2 - Alg] Rewrite: 
[Integral - Alg] Isolate Original Integral: 
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