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Math Help - Integral Help - Trig

  1. #1
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    Integral Help - Trig

    Integral of:

    (tan(x)-1)^2

    Please show major steps. I'm not understanding this. Thanks for your help.
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  2. #2
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    Hello, mathnoob!

    \int (\tan x -1)^2dx

    We have: . (\tan x - 1)^2\:=\:\tan^2\!x-2\tan x + 1 \:=\:(\sec^2x - 1) - 2\tan x + 1

    Then: . \int\left(\sec^2\!x - 2\tan x\right)\,dx

    Can you finish it now?

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  3. #3
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    If I split it up:

    integral(sec(x)^2)dx - integral(2tan(x))dx


    I don't know the integral for sec(x)^2. I do know sec(x), however. That is ln(sec(x)+tan(x)).

    Can this help somehow?
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  4. #4
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    I don't know the integral for sec(x)^2. I do know sec(x), however. That is ln(sec(x)+tan(x)).
    You do know this. What is the derivative of tan x?
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  5. #5
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    Quote Originally Posted by badgerigar View Post
    You do know this. What is the derivative of tan x?
    The derivative of tan(x) is sec(x)^2.

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  6. #6
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    Quote Originally Posted by mathnoob View Post
    The derivative of tan(x) is sec(x)^2.

    What's with the confused emoticon ....???

    If the derivative of tan x is sec^2(x), then clearly the integral of sec^2(x) is tan x.
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  7. #7
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    Oh boy.
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  8. #8
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    integral(sec(x)^2)dx - integral(2tan(x))dx

    tan(x) + C1 + 2ln(cos(x)) + C2

    tan(x) + 2ln(cos(x)) + C

    Is this right? This isn't what my TI-89 is giving me.
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  9. #9
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    Quote Originally Posted by mathnoob View Post
    integral(sec(x)^2)dx - integral(2tan(x))dx

    tan(x) + C1 + 2ln(cos(x)) + C2

    tan(x) + 2ln(cos(x)) + C

    Is this right? This isn't what my TI-89 is giving me.
    that's correct. what does your calculator give you?
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  10. #10
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    Quote Originally Posted by mathnoob View Post
    integral(sec(x)^2)dx - integral(2tan(x))dx

    tan(x) + C1 + 2ln(cos(x)) + C2

    tan(x) + 2ln(cos(x)) + C

    Is this right? This isn't what my TI-89 is giving me.
    It's probably giving you some weird and wonderful answer that is equivalent to tan(x) + 2ln(cos(x)) + C. You can easily check your by-hand answer ...... differentiate it!! You should get the integrand back .....
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