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Integration by substitution: how to ? - Printable Version

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Integration by substitution: how to ? - Aries - 10-10-2014 10:47 AM

A very simple example can be the following: INT(1/(x+SQRT(x)))*dx.
Changing variable u=SQRT(x) --> u^2=x (with u>=0) --> 1/(u^2+u) and dx=2u*dt.
The integral now becomes INT(2u/(u^2+u))*du = INT(2/(u+1))*du = 2*ln |u+1|+c (that is 2*ln |SQRT(x)+1|+c).
How could I do with the Prime ?
TIA,

Aries


RE: Integration by substitution: how to ? - parisse - 10-10-2014 01:37 PM

assume(u>0); a:=subst('integrate(1/(x+sqrt(x)),x)',x=u^2);
a;


RE: Integration by substitution: how to ? - Aries - 10-11-2014 08:16 AM

Thanks Mr Parisse, much appreciated ;-)