What is the integral of $tan (x)$ $tan(x)$ ?

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Answer 1 · 2016-02-20T14:35:48

$\int tan x d x = - ln | cos x | + constant$ $int tanx "d"x = -ln|cosx| + "constant"$

From the chain rule, we know that

$frac{"d"}{"d"x} (ln(f(x))) = frac{1}{f(x)}*f'(x)$

Therefore,

$int frac{f'(x)}{f(x)} "d"x = ln|f(x)| + "Constant"$

We also know that

$frac{"d"}{"d"x}(cosx) = -sinx$

And that

$tanx = frac{sinx}{cosx}$

$= -frac{-sinx}{cosx}$

$= -frac{frac{"d"}{"d"x}(cosx)}{cosx}$

Hence,

$int tanx "d"x = -ln|cosx| + "constant"$

What is the integral of tan(x)tan(x)tan(x)?