Evaluate the indefinite integral by hand:

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(7si{n}^6(x)cos(x))dx$

Evaluate the definite integral by hand:

${\displaystyle \underset{0}{\overset{1}{}}}\frac{2ta{n}^{-1}(x)}{1+x^2}dx$

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