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# integration question watch

1. 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
2. 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)
3. (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)
Thanks mate.

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Updated: February 2, 2006
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