for a certain f(x).
]]>This old post popped up today because of a spammer but I have an answer which might be useful for this:
http://www.mathisfunforum.com/viewtopic.php?pid=316853#p316853
Achchha, how do I integrate tan(x) by hand?
If you start with
and differentiate, you get:
So, when integrating, it is always worth being on the lookout for the presence of a function and its derivative. In your question we have both sine and cosine x , so we do have the function (cos) and its derivative (sin)
By inspection I can see I'm going to need a minus sign too, thus:
A similar argument works for this one:
Substitution for f(x) will always work in these cases (can you see why?) but it takes longer.
Bob
ps. Sometimes I can see an integration 'by inspection'. It's an acceptable method provided you 'prove' your 'guess' actually works by differentiation.
]]>You get -du/u, which you can certainly integrate.
]]>What technique should I use?
]]>Write tan(x) = sin(x)/cos(x).
Then?
Please continue
Achchha, how do I integrate tan(x) by hand?
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