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Section 7.5 : Integrals Involving Roots

Evaluate each of the following integrals.

1. \( \displaystyle \int{{\frac{5}{{4 - \sqrt {3 - z} }}\,dz}}\)
2. \( \displaystyle \int{{\frac{1}{{x + 4\sqrt {x - 3} }}\,dx}}\)
3. \( \displaystyle \int{{\frac{4}{{t - \sqrt {t + 7} + 1}}\,dt}}\)
4. \( \displaystyle \int{{\frac{z}{{2z + 3\sqrt {2z + 1} - 9}}\,dz}}\)
5. \( \displaystyle \int{{\frac{w}{{w - 2\sqrt {6 - 3w} - 5}}\,dw}}\)
6. \( \displaystyle \int{{\cos \left( {\sqrt x } \right)\,dx}}\)