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Des calculs d'intégrales

On tape :
integrate(1/(x^4-1)^10,x);
integrate((x^4+4*x^2+6*x+4)/(x+1)^2,x);
integrate(x/((x-1)*(x+1)^2),x);
integrate(x/((x+1)*(x^4-1)),x);
integrate(1/(3*x*(x^2+x+1)*(x-1)^3),x);
integrate(1/(x^4-1)^2,x);
integrate(1/(x^4+1)^2,x);
integrate(1/(x^4+1)^4,x);
integrate(x^7/((x^4-1)*(x^2+3)),x);
integrate(((1+x)/(1-x))^(1/3),x);
integrate((sin(2*x)+1)/(cos(2*x)),x);
integrate((2*sin(x)+1)/(2*sin(x)-1),x);
integrate(exp(x)/(3+2*exp(x)),x);
integrate(sin(x)^2*cos(x)^4,x);
integrate(sin(x)/(sin(x)^3+cos(x)^3),x);
integrate(1/sqrt(2*x*t)*exp(-t^2/2),x);
integrate(sin(3*x)^4/exp((3*x+1)/cos(t)),x);
integrate(2*x/sqrt(x^2-1),x);
integrate((sin(x)+cos(x))/(sin(x)-cos(x)),x);
integrate(sin(pi/2-2*x),x);
integrate(tan(x)+tan(x)^3,x);
integrate((exp(x)-exp(-x))/(exp(x)+exp(-x)),x);
integrate(1/cos(x)^25,x);
integrate(1/(sin(x)-1)^3,x);
integrate(1/(sin(x)+1)^3,x);
integrate(ln(x+sqrt(1+x^2)),x);
integrate(atan(2*x/(1+x^2)),x);
integrate(x*sqrt(1+x^2),x);
integrate(sin(x)/cos(x)^2,x);
integrate(exp(x)/(1+exp(2*x)),x);
integrate(cos(x/2)^2/(x+sin(x)),x);
integrate(x/sqrt(x+1),x);
integrate(exp(x)/((3+exp(x))*sqrt(exp(x)-1)),x);
integrate(sqrt(x)/sqrt(a^3-x^3),x);
integrate(sqrt(a-x)/sqrt(x),x);
integrate(sqrt(x^2+a^2),x);
integrate(sin(2*x)*cos(x),x);
integrate(x*atan(x),x);
integrate(sinh(x)*cos(x),x);
integrate(atan(x)/x,x);
integrate(1/(sin(x)-2)^3,x);
integrate((2*x^2+1)*exp(x^2),x);
integrate(1/(1+sqrt(1-x^2)),x);
integrate(sin(3*x)/sin(x),x);
integrate(1/(t*ln(t)^2),t,2,x);
integrate(ln(1+2/(n*(n+3))),n,1,+infinity);
integrate((pi*t-t^2)*sin(n*t),t,0,pi);
integrate(exp(t)*cos(n*t),t,-pi,pi);
integrate(exp(x)*sin(x),x,0,t);
integrate(cos(x)/exp(x),x,0,+infinity);
integrate((t^4+t+1)/(t^6+t^3+2),t,1,+infinity);
integrate(1/(t^4+t^2),t,2,+infinity);
integrate(x*exp(1/2*abs(ln(x^2))),x,2,t);
integrate(1/sqrt(2*x*t)*exp(-t^2/2),x,a,b);
integrate((x^2*(1-x))^(1/3),x,0,1);
integrate((a*t+5)/((t-1)^3*(t-2)^2),t,3,x);
integrate(atan(sqrt(1-x^2)),x,0,1);
integrate(ln(x^2+t^2)/(1+t^2),t,0,+infinity);



Documentation de giac écrite par Renée De Graeve