Calcul intégral (1)

1	Énoncé
2	Calculs

1 - Énoncé

(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);

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Source index.txt mouliné par petitParseur(Z+B) le mardi 8 avril 2003.