Home » Blog » Evaluate the integral of arctan x1/2

# Evaluate the integral of arctan x1/2

Evaluate the following integral We use integration by parts, letting Therefore, Now, to evaluate the integral we make the substitution, which implies . Therefore, Plugging this back in to the equation above we obtain,
{"ft_lang_label":"__label__en","ft_lang_prob":0.86456853,"math_prob":0.9965458,"size":435,"snap":"2023-14-2023-23","text_gpt3_token_len":86,"char_repetition_ratio":0.15313224,"word_repetition_ratio":0.9375,"special_character_ratio":0.18620689,"punctuation_ratio":0.175,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9546135,"pos_list":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"im_url_duplicate_count":[null,3,null,3,null,3,null,3,null,5,null,3,null,3,null,3,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2023-06-07T18:21:32Z\",\"WARC-Record-ID\":\"<urn:uuid:33cde20b-1359-4458-b23c-ee12cdabdcce>\",\"Content-Length\":\"59646\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:f049e57c-3deb-4315-948d-ded84aa55be6>\",\"WARC-Concurrent-To\":\"<urn:uuid:504e7284-b2b6-439f-a939-8c047e844390>\",\"WARC-IP-Address\":\"194.1.147.69\",\"WARC-Target-URI\":\"https://www.stumblingrobot.com/2015/11/30/evaluate-the-integral-of-arctan-x12/\",\"WARC-Payload-Digest\":\"sha1:DN2OW44OJVWWXT22NRZCTHZAXXKFWLQJ\",\"WARC-Block-Digest\":\"sha1:LT6P2MBFMZF5CCSQGQFTV6CP7D3MMWS5\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2023/CC-MAIN-2023-23/CC-MAIN-2023-23_segments_1685224654012.67_warc_CC-MAIN-20230607175304-20230607205304-00661.warc.gz\"}"}