# help!! intergration using subWatch

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#1
i just dont get it!!! i was ill when they went through it in the lesson so ive no idea what its about!! i tried reading the text book but it just gave me a headach basically i need to help how to do it than explaining what it is or when to use it. thanks guys!!!
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13 years ago
#2
Example 8 from P3 Book (Edexcel) - P111.

Use the substitution u=cosx to find INT(tanx)dx

INT tanx dx = INT (sinx/cosx) dx

Now, we have to find a way to substitute 'u' into this.

We know that u = cosx

If we're gonna use 'u', we have to change to 'dx' to something in terms of 'du' (since we now want to integrate with respect to u).

So, we differentiate the substitution given:

du/dx = -sinx
Rearrange to make dx the subject: dx = -du/sinx

Now sub in all that you have into the original integral:

INT (sinx/cosx)dx = INT (sinx/u)(-du/sinx) . . . since u=cosx, and dx = -du/sinx

The sinx's cancel, to give:

INT (-1/u)du

= -ln(u) + c

But, u = cosx

So you get: INT (tanx) dx = -ln(cosx) + c
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#3
thanks!!
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