# [Maxima] Unnecessary test in rtest5.mac ?

Dieter Kaiser drdieterkaiser at web.de
Mon Dec 8 17:01:31 CST 2008

```In the test file rtest5.mac problem 48 is declared to be an expected
error. This is the test:

/* test fails because it's not simplified -- do ?print(integrate(%
e^x*erf(x),x)) */

integrate(%e^x*erf(x),x);
%e^x*erf(x)-%e^(1/4)*erf(x-1/2)\$

I do not think that we have an error. The result from the integration is
not as much simplified as possible when we look directly at the
expressions:

integrate(%e^x*erf(x),x);
((MPLUS SIMP)
((MTIMES SIMP) ((MTIMES SIMP) -1 ((MEXPT SIMP) \$%E ((RAT SIMP) 1 4)))
((%ERF SIMP) ((MPLUS SIMP) ((RAT SIMP) -1 2) \$X)))
((MTIMES SIMP) ((MEXPT SIMP) \$%E \$X) ((%ERF SIMP) \$X)))

%e^x*erf(x)-%e^(1/4)*erf(x-1/2);
((MPLUS SIMP)
((MTIMES SIMP) -1 ((MEXPT SIMP) \$%E ((RAT SIMP) 1 4))
((%ERF SIMP) ((MPLUS SIMP) ((RAT SIMP) -1 2) \$X)))
((MTIMES SIMP) ((MEXPT SIMP) \$%E \$X) ((%ERF SIMP) \$X)))

A lot of problems will fail if we do not help Maxima to simplify the
result to get an equal expression.

The next test says:

/* Try again, but ratsimp -- it's not a mathematical error */

ratsimp(integrate(%e^x*erf(x),x) - (%e^x*erf(x)-%e^(1/4)*erf(x-1/2)));
0\$

This example shows that Maxima does the correct integration.

I think we should delete the problem 48 to avoid expected errors which
are not errors. It is an unnecessary test and not an error.

Dieter Kaiser

```