# Calcul intégral (1)

Jean-Michel Sarlat (
jm-sarlat@melusine.eu.org) - 8 avril 2003
 1 Énoncé 2 Calculs

## 2 - Calculs

`(C2) load("integration.mc")\$`
```(C3) integre(1/(t*t^(1/3)),t,1,27);
```

```(C4) integre_chasles((1-abs(x-1))^3,x,0,1,2);
```

```(C5) integre(sqrt(2*x+1),x,0,4);
```

```(C6) integre(x^3*(1-x^2)^(5/2),x,0,1/2);
```

```(C7) integre(1/sqrt(9*x^2+3),x,0,1);
```

```(C8) integre(x^2*sin(x)*exp(x),x,0,%pi/2);
```

```(C9) primitive_simplifie(log(sin(x))/cos(x)^2,x,strig1,expand);
```

```(C10) integre_limite(1/(3*tan(x)+2),x,0,%pi/2);
```

```(C11) block(assume(a>0),integre_chasles_limite(1/(a^2*cos(x)^2+sin(x)^2),x,0,%pi/2,%pi));
```

```(C12) primitive_simplifie(cos(2*x)/(sin(x)+sin(3*x)),x,strig2,radcan);
```

```(C13) primitive_simplifie((1-cos(2*x))/sin(3*x),x,strig2,radcan);
```

```(C14) primitive(1/(2*cosh(x)+sinh(x)+1),x);
```

```(C15) f(x):=((x+1)^(1/2)-(x+1)^(1/3))/((x+1)^(1/2)+(x+1)^(1/3));
```

```(C16) block(assume(t>0),primitive_cv(f(x),x,t-(1+x)^(1/6),t));
```

```(C17) rhs(%)=ev(rhs(%),nouns);
```

```(C18) block(assume(t>0),primitive_cv(sqrt(x^3+1)/x,x,t^2-x^3-1,t));
```

```(C19) rhs(%)=ev(rhs(%),nouns);
```

```(C20) primitive((x+1)/sqrt(x*(1-2*x)),x);
```

```(C21) primitive(sin(2*x)*sinh(3*x),x);
```

```(C22) primitive_cv(tan(x)^5,x,cos(x)-t,t);
```

```(C23) rhs(%)=ev(rhs(%),nouns);
```

```(C24) primitive(sin(x)/(2+tan(x)^2),x);
```

```(C25) primitive(1/(cos(x)^4+sin(x)^4),x);
```

Autres réalisations de ce document : index.pdf, index.ps.
Une archive des sources : index-sources.tgz
Source index.txt mouliné par petitParseur(Z+B) le mardi 8 avril 2003.