integrate with more than two functions linked by a composite function for example : f(g(h(x))) real world example cot^2(2x)
In maths how do you Watch
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- 18-02-2016 18:33
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- 20-02-2016 19:50
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- 20-02-2016 20:21
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 violaLast edited by mstewart91; 20-02-2016 at 20:23.