What is the integral of arctan(x)?

obklopit90r9

obklopit90r9

Answered question

2023-02-15

What is the integral of arctan ( x ) ?

Answer & Explanation

Shiloh Hinton

Shiloh Hinton

Beginner2023-02-16Added 9 answers

I = tan - 1 ( x ) d x
Integrating in pieces:
f ( x ) = tan - 1 ( x )
g ( x ) = 1 , g ( x ) = x
I = x tan - 1 ( x ) - x 1 + x 2 d x
= x tan - 1 ( x ) - 1 2 2 x 1 + x 2 d x
Let u = 1 + x 2
d u = 2 x d x
I = x tan - 1 ( x ) - 1 2 1 u d u
= x tan - 1 ( x ) - 1 2 ln ( | u | )
= x tan - 1 ( x ) - 1 2 ln ( 1 + x 2 ) + C

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