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    How do I integrate tan^3(x) by using a suitable identity?
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    (Original post by Mathematicus65)
    How do I integrate tan^3(x) by using a suitable identity?
    Note that \tan^3 x = \tan x \tan^2 x then use a suitable identity for \tan^2 x
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    (Original post by atsruser)
    Note that \tan^3 x = \tan x \tan^2 x then use a suitable identity for \tan^2 x
    Yeah I did this already to obtain the integral of tanx(sec^2x-1) dx but didn't see how this helped me
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    (Original post by Mathematicus65)
    Yeah I did this already to obtain the integral of tanx(sec^2x-1) dx but didn't see how this helped me
    Note that \int \tan x (\sec^2 x -1) \ dx = \int \tan x \sec^2 x \ dx - \int \tan x \ dx

    What is the relationship between \tan x and \sec^2 x?

    Or alternatively, what is the relationship between \tan x \sec x and \sec x?
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    So you have ∫(tanx(secx)^2-tanx) dx
    notice what happens if you differentiate (secx)^2. You should know the integral of tanx. Now just put those 2 pieces of integration to work out the full integral.
    You can also think about what happens when you differentiate (tanx)^2 and that may help you work out the integral.
 
 
 
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