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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....

When dealing with with mixed fraction operations, the first step is always to change the mixed fraction into a top heavy fraction. Then consider weather the question is a multiplication, divsion, addition...

We can solve this pair of simultaneous equations using substitution. To do this, we firstly have to rearrange one equation to get one variable on its own. For example, we can subtract 2y from each side of...

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)<...