Math Help - Order of integration

If I evaluate an integral

or the constant can be brought outside:
which are different answers, how is this?

Originally Posted by bigdoggy

If I evaluate an integral

or the constant can be brought outside:
which are different answers, how is this?

Would it be because:

since the 3 is absorbed into the constant?

The reason I ask is because I've got this : which can be solved to give different answers:


how can this be so?

Not quite

int(dx/3x) is not ln(3x) but 1/3ln(3x) +c = 1/3ln(x) + c (1/3ln(3)is absorbed into c

To see this differentiate ln(3x) -- you don't get 1/3x

When integrating int(dx/3x) if you leave the 3 in the integral

you should use substitution u = 3x du = 3dx

1/3du = dx and you get 1/3int(1/udu)