4: You get

The first fraction is integrated by substitution. In the second you first get rid of the nine in the denominator, either by factoring out or by the substitution u − 2 = 3z. Then there are three options.

If you remember the reduction formula, use it and the problem is solved. If not, perhaps you remember how the reduction formula was deduced and repeat the process for this particular case. If you have no memory regarding the reduction business, skip it and try a different approach: You face an integral with a power of a quadratics, for which there is a standard method - in this particular case it is the tangent substitution. Here you can even connect this substitution with the simplifying process, namely, you would use the substitution u − 2 = 3tan(t) in the above integral.

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