\Titre{Calcul de primitives} .m load("integration.mc")$ \definecolor{gris}{rgb}{0.6,0.6,0.6} \lstset{xleftmargin=5mm,frame=shadowbox,rulesepcolor=\color{gris}} \lstinputlisting[language=maxima]{integration.mc} .m intdef(1/(t*t^(1/3)),t,1,27); .m intdefChasles((1-abs(x-1))^3,x,0,1,2); .m intdef(sqrt(2*x+1),x,0,4); .m intdef(x^3*(1-x^2)^(5/2),x,0,1/2); .m intdef(1/sqrt(9*x^2+3),x,0,1); .m intdef(x^2*sin(x)*exp(x),x,0,%pi/2); .m primitiveSimp(log(sin(x))/cos(x)^2,x,strig1,expand); .m intconv(1/(3*tan(x)+2),x,0,%pi/2); .m block(assume(a>0),intconvChasles(1/(a^2*cos(x)^2+sin(x)^2),x,0,%pi/2,%pi)); .m primitiveSimp(cos(2*x)/(sin(x)+sin(3*x)),x,strig2,radcan); .m primitiveSimp((1-cos(2*x))/sin(3*x),x,strig2,radcan); .m primitive(1/(2*cosh(x)+sinh(x)+1),x); .m f(x):=((x+1)^(1/2)-(x+1)^(1/3))/((x+1)^(1/2)+(x+1)^(1/3)); .m p:block(assume(t>0),primitiveCV(f(x),x,t-(1+x)^(1/6),t)); .m rhs(p)=ev(rhs(p),nouns); .m p:block(assume(t>0),primitiveCV(sqrt(x^3+1)/x,x,t^2-x^3-1,t)); .m rhs(p)=ev(rhs(p),nouns); .m primitive((x+1)/sqrt(x*(1-2*x)),x); .m primitive(sin(2*x)*sinh(3*x),x); .m p:primitiveCV(tan(x)^5,x,cos(x)-t,t); .m rhs(p)=ev(rhs(p),nouns); .m primitive(sin(x)/(2+tan(x)^2),x); .m primitive(1/(cos(x)^4+sin(x)^4),x);