{"id":19260,"date":"2016-12-24T20:48:16","date_gmt":"2016-12-24T20:48:16","guid":{"rendered":"http:\/\/www.oracletutoring.ca\/blog\/?p=19260"},"modified":"2016-12-24T20:48:16","modified_gmt":"2016-12-24T20:48:16","slug":"calculus-an-arctan-integral","status":"publish","type":"post","link":"https:\/\/www.oracletutoring.ca\/blog\/calculus-an-arctan-integral\/","title":{"rendered":"Calculus:  an arctan integral"},"content":{"rendered":"<h1>The tutor shows the example &#8747;dx\/(x<sup>2<\/sup>+6)<\/h1>\n<p style=\"text-align:center\">&#8747;dx\/(x<sup>2<\/sup>+1) = arctanx + C<\/p>\n<p>The related integral<\/p>\n<p style=\"text-align:center\">&#8747;dx\/(x<sup>2<\/sup>+6)<\/p>\n<p>must be put in the form, as follows:<\/p>\n<p style=\"text-align:center\">&#8747;dx\/(x<sup>2<\/sup>+6) = &#8747;dx\/(6(x<sup>2<\/sup>\/6+1)) = 1\/6 &#8747;dx\/(x<sup>2<\/sup>\/6 + 1)<\/p>\n<p style=\"text-align:center\">=1\/6 &#8747;dx\/((x\/&#8730;6)<sup>2<\/sup>+1) = (&#8730;6)\/6&#8747;(dx(1\/&#8730;6))\/((x\/&#8730;6)<sup>2<\/sup> + 1)<\/p>\n<p>Next it becomes<\/p>\n<p style=\"text-align:center\">1\/&#8730;6&#8747;(dx(1\/&#8730;6))\/((x\/&#8730;6)<sup>2<\/sup> + 1)<\/p>\n<p>which can be integrated:<\/p>\n<p style=\"text-align:center\">1\/&#8730;6 &#8747;(dx(1\/&#8730;6))\/((x\/&#8730;6)<sup>2<\/sup> + 1)=(1\/&#8730;6)arctan(x\/&#8730;6) + C<\/p>\n<p>HTH:)<\/p>\n<p>Source:<\/p>\n<p>Larson, Roland E. and Robert P. Hostetler.  <u>Calculus<\/u>, 3rd ed.  Toronto:  D C Heath and Company, 1989.<\/p>\n<p>Jack of <a href=\"https:\/\/www.oracletutoring.ca\">Oracle Tutoring by Jack and Diane,<\/a> Campbell River, BC.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The tutor shows the example &#8747;dx\/(x2+6) &#8747;dx\/(x2+1) = arctanx + C The related integral &#8747;dx\/(x2+6) must be put in the form, as follows: &#8747;dx\/(x2+6) = &#8747;dx\/(6(x2\/6+1)) = 1\/6 &#8747;dx\/(x2\/6 + 1) =1\/6 &#8747;dx\/((x\/&#8730;6)2+1) = (&#8730;6)\/6&#8747;(dx(1\/&#8730;6))\/((x\/&#8730;6)2 + 1) Next it becomes &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"more-link\" href=\"https:\/\/www.oracletutoring.ca\/blog\/calculus-an-arctan-integral\/\"> <span class=\"screen-reader-text\">Calculus:  an arctan integral<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[234],"tags":[2077],"class_list":["post-19260","post","type-post","status-publish","format-standard","hentry","category-calculus","tag-arctan-integral"],"_links":{"self":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19260","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/comments?post=19260"}],"version-history":[{"count":33,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19260\/revisions"}],"predecessor-version":[{"id":19293,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/posts\/19260\/revisions\/19293"}],"wp:attachment":[{"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/media?parent=19260"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/categories?post=19260"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.oracletutoring.ca\/blog\/wp-json\/wp\/v2\/tags?post=19260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}