Indefinite integral

integrate(x^2,x);

integrate(x^4+2*x+4,x);

integrate(sqrt(x),x);

integrate(sin(x)*cos(x),x);

integrate(%e^(2*x),x);

integrate(%e^(t^2),t);

integrate((sin(x))^3,x);

integrate((b^2-x^2)^(-1/2),x);

integrate(tan(log(x)),x);

integrate(cos(log(x)),x);

Definite integral

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

integrate(x^6+8*x+9,x,0,2);

integrate(sin(x)*cos(x),x,0,%pi);

integrate(%e^(t^2),t,-2,2);

integrate(tan(log(x)),x,1,2);

integrate(sin(log(u)),u,-1,1);

Multiple integrals

integrate(integrate(x^2*y,y,1,2),x,0,3);

integrate(integrate(x^2*y,x,0,3),y,1,2);

integrate(integrate(1-4*x*y,x,0,1),y,1,3);

integrate(integrate(x*sin(y),y,0,%pi/2),x,0,2);

integrate(integrate(x*sin(y),x,0,2),y,0,%pi/2);

Partial fractions

partfrac((3*x+5)/(x^2+3*x+2),x);

partfrac((3*x+1)/(x^2+3*x+2),x);

partfrac((4*x-1)/(x^2-4*x+4),x);

partfrac((x-1)/(x+1)*(x^2+1),x);

partfrac((3*n^2+2*n)/(n^3-3*n^2+2*n-6),n);

partfrac((2*x*y^3-2*y^3+6*x^2*y^2+5*x*y^2-4*x^3*y-2*x^2*y-8*x^4)/(x*y^3-x^2*y^2-2*x^3*y),x);

partfrac((2*x*y^3-2*y^3+6*x^2*y^2+5*x*y^2-4*x^3*y-2*x^2*y-8*x^4)/(x*y^3-x^2*y^2-2*x^3*y),y);

Both side limits

limit(5,x,2);

limit(4*x,x,3);

limit(x+4,x,-1);

limit(t-1,t,2);

limit(sin(theta)/theta,theta,0);

limit(1/x,x,4);

One side limits

limit(log(x),x,0,plus);

limit(x/abs(x),x,0,plus);

limit(x/abs(x),x,0,minus);

limit(x/abs(x),x,0);

integrate(x^2, x);

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