intigrate w.r.t x

Asked by sumahr | 23rd Dec, 2009, 07:10: PM

Expert Answer:

f(x) = sec-1x

Put y = sec-1x; x = sec y; dx = sec y tan y dy = sin y dy/cos2y.

sec-1x dx = y sec y tan y  dy

Integrating by parts,

= y sec y tan y dy - (sec y tan y dy) dy

= y sec y - sec y dy

= y sec y - ln |sec y + tan y| + c

= (sec-1x) x - ln |x + tan sec-1x| + c

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Answered by  | 23rd Dec, 2009, 08:52: PM

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