Integrali

Question

[attach]102726[/attach] Risolvere X SOSTITUZIONE.

cmc · Accepted Answer

Poniamo $ t = x+1 ; ⇒ ; x = t-1 ; ⇒ ; dx = dt $ $  int  frac {x^2}{ sqrt [4]{x+1}} , dx = $ $ =  int  frac {(t-1)^2}{ sqrt [4]{t}} , dx = $ $ =  int (t^2-2t+1) t^{- frac {1}{4}}  , dt = $ $ =  int (t^{ frac {7}{4}} -2t^{ frac {3}{4}}+t^{- frac {1}{4}}) , dt = $  $ =  frac {4}{11} t^{ frac {11}{4}} -2  frac {4}{7} t^{ frac {7}{4}}+ frac {4}{3} t^{ frac {3}{4}} + c = $  $ =  frac {4}{11} (x+1)^{ frac {11}{4}} - frac {8}{7} (x+1)^{ frac {7}{4}}+ frac {4}{3} (x+1)^{ frac {3}{4}} + c = $    $ =  frac {4}{11}  sqrt [4]{(x+1)^{11}} - frac {8}{7}  sqrt [4]{(x+1)^7}+ frac {4}{3}  sqrt [4] {(x+1)^3} + c = $

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