How to Integrate Inverse sine sin^-1(x)

Published On :2020-12-23 05:06:00

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How To Solve  ∫ sin −1 xdx By Parts   u=si n −1 x             dv=1                         du= dx 1− x 2              v=x ∫ sin −1 xdx=x sin −1 x−∫x⋅ 1 1− x 2 dx       By Substitution    Suppose⇒z= x 2                                                                         dz=2 x dx    Now we Have… =x sin −1 x− 1 2 ∫ 1 1−z dz             ⇒x sin −1 x+ 1 2 ⋅2 1−z 1 2 +c                       ⇒x sin −1 x+ 1− x 1 +c MathType@MTEF@5@5@+= feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaaqaaaaa aaaaWdbiaadIeacaWGVbGaam4DaiaacckacaWGubGaam4Baiaaccka caWGtbGaam4BaiaadYgacaWG2bGaamyzaiaaykW7caaMc8Uaey4kIi Vaci4CaiaacMgacaGGUbWdamaaCaaaleqabaWdbiabgkHiTiaaigda aaGccaWG4bGaaeizaiaadIhaaeaacaWGcbGaamyEaiaabccacaWGqb GaamyyaiaadkhacaWG0bGaam4CaiaaykW7caaMc8UaaGPaVlaadwha cqGH9aqpcaWGZbGaamyAaiaad6gapaWaaWbaaSqabeaapeGaeyOeI0 IaaGymaaaakiaadIhacaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaa ykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Uaam izaiaadAhacqGH9aqpcaaIXaaabaGaaGPaVlaaykW7caaMc8UaaGPa VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8 UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7 caaMc8UaaGPaVlaaykW7caaMc8UaaeizaiaadwhacqGH9aqpdaWcaa WdaeaaqaqrbKFapdWdciaadsgacaWG4baapaqaa8qadaGcaaWdaeaa piGaaGymaiabgkHiTiaadIhapaWaaWbaaSqabeaapiGaaGOmaaaaa8 qabeaaaaGccaaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaamODaiabg2 da9iaadIhaaeaacqGHRiI8ciGGZbGaaiyAaiaac6gapaWaaWbaaSqa beaapeGaeyOeI0IaaGymaaaakiaadIhacaqGKbGaamiEaiabg2da9i aadIhaciGGZbGaaiyAaiaac6gapaWaaWbaaSqabeaapeGaeyOeI0Ia aGymaaaakiaadIhacqGHsislcqGHRiI8piGaamiEaiabgwSix=qada WcaaWdaeaapiGaaGymaaWdaeaapeWaaOaaa8aabaWdciaaigdacqGH sislcaWG4bWdamaaCaaaleqabaWdciaaikdaaaaapeqabaaaaOWdci aabsgacaWG4baabaWdbiaacckacaGGGcGaaiiOaiaacckacaGGGcGa aiiOaiaadkeacaWG5bGaaeiiaiaadofacaWG1bGaamOyaiaadohaca WG0bGaamyAaiaadshacaWG1bGaamiDaiaadMgacaWGVbGaamOBaiaa ykW7caaMc8UaaGPaVlaaykW7caWGtbGaamyDaiaadchacaWGWbGaam 4BaiaadohacaWGLbGaeyO0H4TaamOEaiabg2da98GacaWG4bWdamaa CaaaleqabaWdciaaikdaaaaak8aabaGaaGPaVlaaykW7caaMc8UaaG PaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaayk W7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPa VlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8 UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7 caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVl aaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8Ua aGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7ca aMc8UaaGPaVlaaykW7caaMc8+dbiaadsgacaWG6bGaeyypa0JaaGOm aiaacckacaWG4bGaaiiOaiaadsgacaWG4baabaGaaGPaVlaaykW7ca aMc8UaamOtaiaad+gacaWG3bGaaeiiaiaadEhacaWGLbGaaeiiaiaa dIeacaWGHbGaamODaiaadwgacqGHMacVaeaacqGH9aqpcaWG4bGaci 4CaiaacMgacaGGUbWdamaaCaaaleqabaWdbiabgkHiTiaaigdaaaGc caWG4bGaeyOeI0YaaSaaa8aabaWdciaaigdaa8aabaWdciaaikdaaa WdbiabgUIiYpaalaaapaqaa8GacaaIXaaapaqaa8qadaGcaaWdaeaa piGaaGymaiabgkHiTiaadQhaaSWdbeqaaaaak8GacaqGKbGaamOEa8 qacaGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaacckaaeaacaaMc8Ua aGPaVlaaykW7caaMc8UaaGPaVlaacckacqGHshI3caWG4bGaci4Cai aacMgacaGGUbWdamaaCaaaleqabaWdbiabgkHiTiaaigdaaaGccaWG 4bGaey4kaSYaaSaaa8aabaWdciaaigdaa8aabaWdciaaikdaaaGaey yXICTaaGOma8qadaqadaWdaeaapiGaaGymaiabgkHiTiaadQhaa8qa caGLOaGaayzkaaWdamaaCaaaleqabaWdbmaalaaapaqaa8GacaaIXa aapaqaa8GacaaIYaaaaaaak8qacqGHRaWkcaWGJbGaaiiOaiaaccka caGGGcGaaiiOaiaacckacaGGGcGaaiiOaiaacckacaGGGcGaaiiOaa qaaiaaykW7caaMc8UaaGPaVlaaykW7caaMc8UaaGPaVlaaykW7caaM c8UaaGPaVlaaykW7caaMc8UaaiiOaiabgkDiElaadIhaciGGZbGaai yAaiaac6gapaWaaWbaaSqabeaapeGaeyOeI0IaaGymaaaakiaadIha cqGHRaWkdaGcaaWdaeaapeGaaGymaiabgkHiTiaadIhapaWaaWbaaS qabeaapeGaaGymaaaaaeqaaOGaey4kaSIaam4yaaaaaa@F570@