### The Maxima on-line user's manual

Algebra Calculator

#### Risch

Function: risch (<expr>, <x>) Integrates <expr> with respect to <x> using the transcendental case of the Risch algorithm. (The algebraic case of the Risch algorithm has not been implemented.) This currently handles the cases of nested exponentials and logarithms which the main part of `integrate` cant do. `integrate` will automatically apply `risch` if given these cases.

`erfflag`, if `false`, prevents `risch` from introducing the `erf` function in the answer if there were none in the integrand to begin with.

```          (%i1) risch (x^2*erf(x), x);
2
3                      2                - x
%pi x  erf(x) + (sqrt(%pi) x  + sqrt(%pi)) %e
(%o1)   -------------------------------------------------
3 %pi
(%i2) diff(%, x), ratsimp;
2
(%o2)                       x  erf(x)```

```(%o1)                                true
(%i2) ```

### Related Examples

##### risch

risch(e^x/(1-e^2*x),x);

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##### risch

risch((x^2-x^3)^(-1/3...

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? risch;

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##### risch-sqrt

risch(sqrt(x+sqrt(x))...

Calculate

##### risch-sqrt

risch ((x^2 + 2*x + 1...

Calculate

##### risch

risch(e^x/(1-e^2*x),x);

Calculate

##### risch

risch((x^2-x^3)^(-1/3...

Calculate

? risch;

Calculate

##### risch-sqrt

risch(sqrt(x+sqrt(x))...

Calculate

##### risch-sqrt

risch ((x^2 + 2*x + 1...

Calculate