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When we integrate by parts, we begin by setting the first term to equal some variable U, the second term in the integral we set to be dv/dx. Then we differentiate the U to obtain du/dx and integrate dv/dx...

tanx = 4cotx + 3  - Multiply through by tan to form a quadratic. tan^2x = 4 + 3tanx - Simplify by allowing y to equal tanx. y^2 = 4 + 3y - Rearange to standard quadratic form. y^2 - 3y -4 = 0 - Factorise....

First we follow the "times by the power and take one from the power" rule. This is the easiest way to remember how to differentiate anything. 

So (3x4)x^(4-1) -(2x2)x^(2-1)<...