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# In maths how do you Watch

1. integrate with more than two functions linked by a composite function for example : f(g(h(x))) real world example cot^2(2x)

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3. Usually you'd do this with a substitution, i.e. u = h(x). In the case of cot^2(2x), apply u = 2x and du = 2dx to give:

1/2 * cot^2(u) du. Then use cot^2(x) = csc^2(x) - 1, giving: (1/2) * [csc^2(u) - 1] du.

Integrating this is then relatively trivial, since the integral of csc^2(x) is -cot(x), leading to:

(1/2) * (-cot(u) - u). Then substitute u back in to give: (1/2) * (-cot(2x) - 2x) -> -0.5cot(2x) - x + C. et viola

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Updated: February 20, 2016
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