Help me find the anitderivative of this

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SUMMARY

The antiderivative of the function tan(x)/sec^99(x) can be simplified using the identity tan(x) = sin(x)/cos(x) and the reciprocal sec(x) = 1/cos(x). By substituting u = sec(x), the integral becomes more manageable, allowing for straightforward integration techniques. This method effectively transforms the original function into a simpler form suitable for integration.

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  • Familiarity with u-substitution in integral calculus.
  • Basic knowledge of antiderivatives and integration techniques.
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What is the antiderivative of tanx/sec^99x?
 
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tan(x) = sin(x)/cos(x)
1/sec(x) = cos(x)

tan(x)/sec^99(x) =...?

A simple u-sub should pop right out once you simplify this.
 
Make the substitution [tex]u=\sec x[/tex]
 

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