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    integrate
    sex^4 dx

    u=tanx

    i attempted this question and got as far as this

    -sec^2 x du

    what do i do next or am i on the right lines?
    thankx
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    (Original post by diggingupworms)
    integrate
    sex^4 dx

    u=tanx

    i attempted this question and got as far as this

    -sec^2 x du

    what do i do next or am i on the right lines?
    thankx
    I hope that's not a minus sign you have there!

    Do you know an identity connecting sec and tan?
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    (Original post by ghostwalker)
    I hope that's not a minus sign you have there!

    Do you know an identity connecting sec and tan?
    the diffential of tanx is -sec^2 x
    so i divded it
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    (Original post by diggingupworms)
    the diffential of tanx is -sec^2 x
    so i divded it
    the differential of tanx is sec^2 x without the -ve sign.
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    (Original post by KeineHeldenMehr)
    the differential of tanx is sec^2 x without the -ve sign.
    o
    yeah so you would get

    after

    sec^2 x du
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    u = tan x
    du/dx = sec^2 x
    du = sec^2 x dx

    integrate tan x = integrate tan x (sec^2 x ) dx
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    ok,

    u =tanx

    i'm going to use "S" as an integrating sign just did speed things up.
    S (sec^4 x)dx
    =S((sec^2 x)(sec^2 x)dx

    now with u=tanx

    we differentiated du/dx=sec^2x
    so du=(sec^2x)dx

    so, S((sec^2 x)du

    from here just use u^2=tan^2x, (which is your substitution squared on both sides) and the identity tan^2x+1 = sec^2x

    should give you S(u^2+1)du - integrate it!

    then replace u with your substitution.
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    (Original post by KeineHeldenMehr)
    ok,

    u =tanx

    i'm going to use "S" as an integrating sign just did speed things up.
    S (sec^4 x)dx
    =S((sec^2 x)(sec^2 x)dx

    now with u=tanx

    we differentiated du/dx=sec^2x
    so du=(sec^2x)dx

    so, S((sec^2 x)du

    from here just use u^2=tan^2x, (which is your substitution squared on both sides) and the identity tan^2x+1 = sec^2x

    should give you S(u^2+1)du - integrate it!

    then replace u with your substitution.
    THANK YOU! x
 
 
 
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