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

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