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+--- Thread: Integration by substitution: how to ? (/thread-2265.html)
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 ;-)