prove antiderivative formula integral of sec u du

[chaoticsouls]

Complete and Pove this antiderivative formula Integral(Sorry don't know how to do actual symbol of) sec u du

 

[o_O]

Re: antiderivative help

Hmm, you're asked to prove something but all you're given an integral to find.

Anyhow, this is a pretty standard integral:

\(\displaystyle \int secx dx = ln (secx + tanx) + C \quad \quad \mbox{(Those should be absolute value signs)}\)

The trick is to multiply secx by (secx + tanx) / (secx + tanx) and perform the appropriate u-substitution.

\(\displaystyle \int secx dx = \int secx \cdot \frac{secx + tanx}{secx + tanx} dx\)

And so on.