Method of substitution (Cancelling Method) Notes

Evaluate the following integrals.

1. \({\displaystyle\displaystyle \displaystyle\int \frac{(\ln x)^4}{x} \mathrm{ d}x}\)
2. \({\displaystyle\displaystyle \displaystyle\int \frac{1}{x(1 - \ln x)} \mathrm{ d}x}\)
3. \({\displaystyle\displaystyle \displaystyle\int \frac{1}{x\sqrt{1 - \ln x}} \mathrm{ d}x}\)
4. \({\displaystyle\displaystyle \displaystyle\int \frac{(3 - \sqrt{x})^5}{\sqrt{x}} \mathrm{ d}x}\)
5. \({\displaystyle\displaystyle \displaystyle\int \frac{1}{\sqrt{x}(1 - \sqrt{x})} \mathrm{ d}x}\)
6. \({\displaystyle\displaystyle \displaystyle\int \frac{1}{\sqrt{x}(\sqrt{x} + 1)^5} \mathrm{ d}x}\)