1. Evaluate the following integral : (a) ( int frac{sec ^{4}(2 t)}{ an ^{9}(2 t)} d t )
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Recall that \(\sec(x) = \frac{1}{\cos(x)}\) and \(\tan(x) = \frac{\sin(x)}{\cos(x)}\). So we can rewrite the integral as follows: \[ \int \frac{\sec^{4}(2t)}{\tan^{9}(2t)} dt = \int \frac{\cos^{-4}(2t)}{\left(\frac{\sin(2t)}{\cos(2t)}\right)^{9}} dt \] Show more…
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