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 U-Substitution of sec^2(x)tan(x)

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I'm trying to calculate the following integral using u-substitution:

 

\(\int sec^2(x)tan(x) dx\)

 

I've came up with

 

\(u = tan(x)\)

\(du = sec^2(x)dx\)

 

Making my formula now:

 

\(\int u du\)

 

And this is about where i'm stuck :\ not really sure what to do for the next step. Any help appreciated guys.

 Aug 28, 2016

Best Answer 

 #1
avatar+33661 
+5

Try it this way:

 

.

 Aug 28, 2016

3+0 Answers

 #1
avatar+33661 
+5
Best Answer

Try it this way:

 

.

Alan Aug 28, 2016
 #2
avatar
0

\(\displaystyle \int{udu}=u^{2}/2 +C=(1/2)\tan^{2}x+C\)

.
 Aug 28, 2016
 #3
avatar+33661 
+5

The above two answers look different but they are the same to within an arbitrary constant:

 

sin2x + cos2x = 1

 

Divide by cos2x

 

tan2x + 1 = 1/cos2x

 

or:   tan2x + 1 = sec2x

Alan  Aug 29, 2016

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