NJC Integration Techniques Tutorial Q3

Find the following integrals using integration by parts.

1. \(\displaystyle\displaystyle \displaystyle\int{x{{\sec }^{2}}x\,\mathrm{d}x}\)
2. \(\displaystyle\displaystyle \displaystyle\int{\sec x\tan x\ln \left( \sec x \right)}\,\mathrm{d}x\)
3. \(\displaystyle\displaystyle \displaystyle\int{x{{\sin }^{2}}x\,\mathrm{d}x}\)
4. \(\displaystyle\displaystyle \displaystyle\int{2x{{\cos }^{2}}x\,\mathrm{d}x}\)
5. \(\displaystyle\displaystyle \displaystyle\int{x\sin x\cos x\,\mathrm{d}x}\)