# Another Integration by Parts problem I keep getting almost right!

• Feb 21st 2010, 02:37 PM
s3a
Another Integration by Parts problem I keep getting almost right!
My work is attached.

The final answer in my text book is the same that Wolfram Alpha provides:
integral (arctan(4x - Wolfram|Alpha))

but Wolfram Alpha does not show the work for this integThe final answer in my text book is the same that Wolfram Alpha provides:ral; it says "\$Aborted" whenever I ask it to show the steps.

My work is different according to this in Wolfram Alpha: is 1/8 * ln(1 + 16x^2) = 2ln(x^2 +1) ?

If they are equal, it returns true, otherwise it shows the usual data. And, it does not return true, so they are not equal.

Any help would be very much appreciated!
Thanks!
• Feb 21st 2010, 02:48 PM
jiboom
Quote:

Originally Posted by s3a
My work is attached.

The final answer in my text book is the same that Wolfram Alpha provides:
integral (arctan(4x - Wolfram|Alpha))

but Wolfram Alpha does not show the work for this integThe final answer in my text book is the same that Wolfram Alpha provides:ral; it says "\$Aborted" whenever I ask it to show the steps.

My work is different according to this in Wolfram Alpha: is 1/8 * ln(1 + 16x^2) = 2ln(x^2 +1) ?

If they are equal, it returns true, otherwise it shows the usual data. And, it does not return true, so they are not equal.

Any help would be very much appreciated!
Thanks!

you have differentiated arctan(4x) wrongly.

it should be

4/(16x^2+1)
• Feb 21st 2010, 02:49 PM
o_O
You made an error when you took the derivative of $\tan ^{-1} (4t)$
• Feb 21st 2010, 07:04 PM
s3a
Omg! I would have never spotted that mistake! Thanks to both of you! (I had forgotten that you replace the contents of arctan into the x)