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

Algebra Calculator

#### Changevar

Function: changevar (<expr>, <f(x,y)>, <y>, <x>) Makes the change of variable given by `<f(x,y)> = 0` in all integrals occurring in <expr> with integration with respect to <x>. The new variable is <y>.

```          (%i1) assume(a > 0)\$
(%i2) integrate (%e**sqrt(a*y), y, 0, 4);
4
/
[    sqrt(a) sqrt(y)
(%o2)                I  %e                dy
]
/
0
(%i3) changevar (%, y-z^2/a, z, y);
0
/
[                abs(z)
2 I            z %e       dz
]
/
- 2 sqrt(a)
(%o3)            - ----------------------------
a```

An expression containing a noun form, such as the instances of integrate above, may be evaluated by `ev` with the `nouns` flag. For example, the expression returned by `changevar` above may be

`     evaluated by `ev (%o3, nouns)`.`

`changevar` may also be used to changes in the indices of a sum or product. However, it must be realized that when a change is made in a sum or product, this change must be a shift, i.e., `i = j+ ...`, not a higher degree function. E.g.,

```          (%i4) sum (a[i]*x^(i-2), i, 0, inf);
inf
====
\         i - 2
(%o4)                     >    a  x
/      i
====
i = 0
(%i5) changevar (%, i-2-n, n, i);
inf
====
\               n
(%o5)                    >      a      x
/        n + 2
====
n = - 2```

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

### Related Examples

##### changevar-integrate-kill-nouns-sin-tan

kill(all);

changevar(integrate(1...

ev(%,nouns);

Calculate

##### changevar-integrate-nouns-sin-tan

changevar('integrate(...

ev(%,nouns);

Calculate

##### changevar-diff-integrate-ratsimp

integrate(x/(x^3+1),x);

ratsimp (diff(integra...

a:integrate(1/((x-3)^...

Calculate

##### changevar-cos-integrate-logabs-sin-true

logabs:true;

i = 'integrate(1/sin(...

eq:t=cos(x);

Calculate

##### changevar-diff-integrate-ratsimp

integrate(x/(x^3+1),x);

ratsimp (diff(integra...

a:integrate(1/((x-3)^...

Calculate

##### changevar-sum

changevar (sum (i^2, ...

Calculate

##### changevar

changevar (%, y-z^2/a...

Calculate

##### changevar-cos-erf-integrate-nouns-phi-pi-sin

kerf(x):=(sin(theta)/...

I:'integrate(kerf(x),...

I:changevar(I,y-sin(t...

Calculate

##### changevar-integrate

'integrate(2*x*(x^2+1...

changevar(%, x^2+1-t,...

Calculate

##### changevar-inf-integrate-solve-sqrt

'integrate((x+(x^2+1)...

solve(u-(sqrt(x^2+1)+...

changevar(%,u-(sqrt(x...

Calculate