How do you find ∫arctanx?
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Apply Integration By Parts : u =arctan( x ), v ′=1. = x arctan( x )−∫ x x 2+1 dx.
∫ x x 2+1 dx =12 ln| x 2+1| = x arctan( x )−12 ln| x 2+1|
= x arctan( x )−12 ln| x 2+1|+ C.
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★Heya★
integration of Tan-¹ x dx can be calculated by using integration by parts rule.
=>
Integration of 1 × Tan-¹ x dx
=>
x Tan-¹ x - Integration of ( x/ ( 1+ x² )
=>
x Tan-¹ x - 1/2 ( log ( 1 + x² ) )
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