Integrate the function in x tan-1 x. - Mathematics

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Sum

Integrate the function in x tan-1 x.

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Solution

Let `I = int x tan^-1 x dx`

`= tan^-1 x int x  dx - int [(d/dx(tan^-1 x)) int (x  dx)]  dx`

`= tan^-1 x (x^2/2) - int 1/ (1 + x^2) * x^2/2 dx`

`= x^2/2 tan^-1 x - 1/2 int x^2/ (x^2 + 1) dx`

`= x^2/2 tan^-1 x - 1/2 int (x^2 + 1 - 1)/ (1 + x^2)  dx`

`= x^2/2 tan^-1 x - 1/2 int (1 - 1/(1 + x^2)) dx`

`= x^2/2 tan^-1 x - 1/2 (x - tan^-1 x) + C`

`= x^2/2 tan^-1 x - 1/2 x + 1/2 tan^-1 x + C`

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Chapter 7: Integrals - Exercise 7.6 [Page 327]

APPEARS IN

NCERT Mathematics Class 12
Chapter 7 Integrals
Exercise 7.6 | Q 8 | Page 327

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