Please Do this integration for me!

AIEEE Papers › Calculus questions › Please Do this integration for me!

\int \left(tan^{-1}x \right)^{2}dx

#Mathematics #Calculus

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11 Answers

1

Vinay Arya ·2011-03-18 04:35:49

I=âˆ«(tan^-1x)²dx
Integration by parts
I=x(tan^-1)²-âˆ«2xtan^-1x1+x²dx
I'=âˆ«2xtan^-1x1+x²dx
tan^-1x=t
dx=(1+x²)dt
I'=2âˆ«t tant dt
I'=2tlog!sect!-2âˆ«log!sect!dt
I'=2tlog!sect!-2tlog!sect!-âˆ«t tantdt
I'=-4tlog!sect!-I'/2
I'=8tlog!sect!/3
I=x(tan^-1x)²-8tlog!sect!/3 +C

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1

swordfish ·2011-03-18 05:17:16

@ Vinay
which software do you use for writing the HTML math?

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1

Vinay Arya ·2011-03-18 05:19:07

I do not use any software.Whatever facility is given on this forum I use it.

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1

Ricky ·2011-03-18 06:50:39

Vinay , in line no. 9 , you get

I ' = 2 t log ( sec t ) - 2 t log ( sec t ) + I ' ........................ : )

You have part integrated taking one function , then again part integrated taking the other function , which leaves you at -

I ' = I '

Actually , this is an un - integrable function . You cannot find its antiderivative in terms of known functions . The actual answer may be verified at -

http://integrals.wolfram.com/index.jsp?expr=%7BArcTan%5Bx%5D%7D%5E2&random=false

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49

Subhomoy Bakshi ·2011-03-18 07:56:06

@Soumya: This is an AISSCE question! :P
:P

This is then a sure boomerang! must be awarding free +6 to all??

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39

Pritish Chakraborty ·2011-03-18 08:44:50

This came in the boards some years back and if I remember correctly, there was controversy regarding it. Surely +6 to all.

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21

Shubhodip ·2011-03-18 08:46:39

I wonder how wolfram does integrations like that!!!!

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1

swordfish ·2011-03-18 11:02:15

Damn!! I never saw the fraction button.

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1

anishvarsha iska ·2011-08-05 17:53:25

use the following word to solve by parts
ILATE

I - Inverse trignometric functions
L - Logarithmic functions
A - Arithmatics
T - Trignometric functions
E - Exponential functions

take the above functions values by u

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71

Vivek @ Born this Way ·2011-08-08 06:31:46

@anish.. Yeah that is okay, But it won't work here.. You can even try âˆ«x tanx dx

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1

jee12 ·2011-08-10 21:39:21

is it not possible to integrate this function ???

âˆ« log (cosx) dx

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Your Answer

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