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https://texercises.com/exercise/sostituzione-8/
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Exercise:
frac+x^^tfracdx Sfruttando la sostituzione xtanu

Solution:
Abbiamo che dx+tan^udu dunque l'egrale diventa frac+x^^tfracdx frac+tan^u^tfrac +tan^udufrac frac+tan^u^/du ma siccome +tan^ufraccos^u l'egrale diventa frac+x^^tfracdxfrac cosudufracsinu+Cfracsinleftarctanlefttfracxrightright+C e da ultimo siccome sinarctanxfracxsqrt+x^ insero fracx otteniamo frac+x^^tfracdxfracfracxsqrt+x^+C
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Exercise:
frac+x^^tfracdx Sfruttando la sostituzione xtanu

Solution:
Abbiamo che dx+tan^udu dunque l'egrale diventa frac+x^^tfracdx frac+tan^u^tfrac +tan^udufrac frac+tan^u^/du ma siccome +tan^ufraccos^u l'egrale diventa frac+x^^tfracdxfrac cosudufracsinu+Cfracsinleftarctanlefttfracxrightright+C e da ultimo siccome sinarctanxfracxsqrt+x^ insero fracx otteniamo frac+x^^tfracdxfracfracxsqrt+x^+C
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Attributes & Decorations
Tags
Calcolo integrale, Sostituzione
Difficulty
(1, default)
Points
0 (default)
Language
ITA (Italiano)
Type
Calculative / Quantity
Decoration
Content image