# How do you integrate #int 1/(4-x)^(3)dx# using trigonometric substitution?

The answer is

We need

You can perform this integral without using trigonometric substitution, we apply simple substitution

Therefore,

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To integrate (\int \frac{1}{(4-x)^3} , dx) using trigonometric substitution, you can make the substitution (x = 4 - \tan^2(\theta)), which will lead to a form that can be integrated using trigonometric identities. After making this substitution, you can then express (dx) in terms of (\theta), and rewrite the integral in terms of (\theta). Finally, you can integrate with respect to (\theta), then substitute back the original variable (x).

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