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    :confused: Can someone show me how to do the following question please.

    Use a) differentiation b) integration by parts to prove

    (integral) arcsec x dx = xarcsec x - ln(x + (x^2 - 1)^0.5) + C

    Thanks
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    i) Differentiate RHS to prove the integral
    ii) Take du/dx=1 and v=arcsecx
    Then u=x and dv/dx=1/{x.sqrt(x^2-1)} (show this by writing secy=x and differentiating implicitly)
    Apply parts to give:
    I = xarcsecx-INT 1/{sqrt(x^2-1)} dx = xarcsecx - arcoshx + C

    and arcoshx = ln[x+sqrt(x^2-1)] (FP2)
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    (Original post by C4>O7)
    i) Differentiate RHS to prove the integral
    ii) Take du/dx=1 and v=arcsecx
    Then u=x and dv/dx=1/{x.sqrt(x^2-1)} (show this by writing secy=x and differentiating implicitly)
    Apply parts to give:
    I = xarcsecx-INT 1/{sqrt(x^2-1)} dx = xarcsecx - arcoshx + C

    and arcoshx = ln[x+sqrt(x^2-1)] (FP2)
    :yy: Thanks mate.
 
 
 
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