Techniques of Integration - Cyclic Integration by Parts

1. \(\displaystyle \displaystyle\int{x\sin 3x\,\mathrm{d}x}\)
2. \(\displaystyle \displaystyle\int{x\ln x\,\mathrm{d}x}\)
3. \(\displaystyle \displaystyle\int{\ln x\,\mathrm{d}x}\)
4. \(\displaystyle \displaystyle\int{\frac{\ln x}{x}\,\mathrm{d}x}\)
5. \(\displaystyle \displaystyle\int{\sin (\ln x)\,\mathrm{d}x}\)

6. \(\displaystyle \displaystyle\int{{{2}^{\ln x}}\,\mathrm{d}x}\)
7. \(\displaystyle \displaystyle\int{{{\tan }^{-1}}x\,\mathrm{d}x}\)
8. \(\displaystyle \displaystyle\int{x{{\sin }^{2}}x\,\mathrm{d}x}\)
9. \(\displaystyle \displaystyle\int{\frac{x}{{{\cos }^{2}}5x}\,\mathrm{d}x}\)

10. \(\displaystyle \displaystyle\int{\text{cose}{{\text{c}}^{3}}x\,\mathrm{d}x}\)
11. \(\displaystyle \displaystyle\int{\frac{1}{{{\cos }^{3}}3x}\,\mathrm{d}x}\)
12. \(\displaystyle \displaystyle\int{\sec x\tan x{{e}^{\text{sec}x}}\,\mathrm{d}x}\)