#### 6.72 Assume(16.2.01)

##### 6.72.1 John Trapp

I am sure that this has been reported before.

> assume(-3<t);additionally(t<3);
Originally t, renamed t~:
is assumed to be: RealRange(Open(-3),Open(3))

> int(2/(t^2-9),t);

> int(-2/(9-t^2),t);

> -int(2/(9-t^2),t);



In each case the solution is 1/3ln(t~-3)-1/3ln(t~+3). Maple does not recognize the domain of the integrand at all and we have the log of a negative number. Ugly.

##### 6.72.2 Carl DeVore (19.2.01)

If you allow for the constant of integration to be complex, then the result makes sense. If you evaluate this anitiderivative between real limits, you will get a real answer.

I do realize, however, that this is diﬃcult to explain to a beginning calculus student when you’re trying to teach them Maple.

##### 6.72.3 E. Elbraechter (20.2.01)

Note that no constant of integration appears in the result.

Therefore the integral of an real valued integrand can have a constant imaginary part;

> restart;
> assume(-3<t, t<3);
>   int(2/(t^2-9),t):
>   evalc(%):
> J  := %;
J := 1/3 ln(3 - t) - 1/3 ln(t + 3) + 1/3 I Pi

> Jr := Re(J);
Jr := 1/3 ln(3 - t) - 1/3 ln(t + 3)



For -3 < t < 3 this is a real valued expression.

##### 6.72.4 Adri van der Meer (20.2.01)

Try:

> f := int(2/(x^2-9),x=0..t);



and Maple will recognize the assumption made on t.