Question

integrate integral sec^2 3 xdx /1+4tan3x

Answer 1

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Answer 2

Try substituting the bottom

Answer 3

\[\int\frac{\sec^23x}{1+4\tan3x}~dx\]
Let \(u=1+4\tan 3x\), so \(\dfrac{1}{12}du=\sec^23x~dx\):
\[\frac{1}{12}\int\frac{du}{u}\]