Antiderivative of arctan ⁡ ( − x 2 ).As I said in the title I'm...

Kiana Dodson

Kiana Dodson

Answered

2022-06-29

Antiderivative of arctan ( x 2 ).
As I said in the title I'm trying to find an antiderivative of f ( x ) = arctan ( x 2 ).
I am aware that e.g. WolframAlpha can find one, but I have no clue how to do it by hand. Can anyone give me a hint?

Answer & Explanation

britspears523jp

britspears523jp

Expert

2022-06-30Added 28 answers

Step 1
If you integrate by parts, you get arctan ( x 2 ) d x = x arctan ( x 2 ) x 2 x 1 + x 4 d x
Step 2
Now find the partial fraction decomposition 2 x 2 1 + x 4 = A x + B x 2 + x 2 + 1 + C x + D x 2 x 2 + 1 and the rest is standard.

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