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Exercise

$\int\left(1+\sqrt[2]{\tan\left(x\right)}\right)^2\sec^2\left(x\right)dx$

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Final answer to the exercise

$\frac{1}{2}\left(1+\sqrt{\tan\left(x\right)}\right)^{4}-\frac{2}{3}\left(1+\sqrt{\tan\left(x\right)}\right)^{3}$

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