What is the integral of #tan(x)#?
1 Answer
Feb 20, 2016
Explanation:
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"#