I am having an issue with this problem.(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\int tan(x)^3: [/tex]

You separate a tan(x)^2, and use the identity 1+tan(x)^2 = sec(x)^2

You then end up with [tex]\int tan(x) sec(x)^2 dx[/tex] + [tex]\int tan(x) dx[/tex]

[tex]\int tan(x) dx = ln absval(sec(x)) [/tex]

[tex]\int tan(x) sec(x)^2 dx[/tex]

Here, the book says to solve the problem this way:

set u = tan(x) du = sec(x)^2dx

so [tex]\int u du = 1/2 u ^2 = 1/2 tan(x)^2 [/tex]

Why can't you solve this problem this way instead?

[tex]\int (tan(x) sec(x)) sec(x) dx[/tex]

set u = sec(x), du = (tan(x) sec(x)) dx

so [tex]\int u du = 1/2 u ^2 = 1/2 sec(x)^2 [/tex]

I think I must be missing something...any help you could give me would be greatly appreciated.

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# Integral of tan(x)^3

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