Integration problem

Asked by  | 2nd Jan, 2010, 12:37: PM

Expert Answer:

Let's put y = tan-1x

tan y = x

tan2 y = x

2 tany sec2y dy = dx

 tan-1x dx = 2y tany sec2y dy

= y tan2y - tan2y dy + c  ...........integrating by parts

= y tan2y - (sec2y  - 1)dy + c

= y tan2y - tan y + y + c

= tan-1x tan2(tan-1x) - tan (tan-1x) + tan-1x + c

= x tan-1x  - x + tan-1x + c

Regards,

Team,

TopperLearning.

Answered by  | 2nd Jan, 2010, 01:50: PM

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