(%i1) integrate(integrate(1/(1-x*y),y,0,1),x,0,1);

Result

(%i2) integrate(integrate(1/sqrt(1-x^2*y^2),y,0,1),x,0,1);

Result

(%i3) asin(x)*log(1 - exp((2*%i)*asin(x)))
 - (%i/2)*(asin(x)^2 + li[2](exp((2*%i)*asin(x))));
4*(subst(1,x,%) - limit(%, x, 0, plus));

Result

(%i5) integrate(integrate(1/sqrt(2-x-y),y,-1,1),x,-1,1);

Result

(%i6) ( 16 / 3 ) * ( 2 - sqrt ( 2 ) );
expand(-(2^(9/2)-32)/3 - %);

Result

(%i8) integrate(integrate(1/sqrt(3-x-2*y),y,-1,1),x,-1,1);

Result

(%i9) ( sqrt ( 32 ) / 3 ) * ( sqrt ( 27 ) - sqrt ( 8 ) - 1 );
radcan(factor(% - (2*6^(3/2)-2^(5/2)-16)/3));

Result

(%i11) integrate(integrate(sqrt(x*y),y,0,1),x,0,1);

Result

(%i12) integrate(integrate(exp(-((x-4)^2+(y-1)^2)),y,0,5),x,0,5);
factor(%);

Result

(%i14) integrate(integrate(sqrt((x^2 + y^2 - 1/4)^2),y,0,1),x,0,1);
integrate(integrate((r^2-1/4)*r,r,1/2,sec(theta)),theta,0,%pi/4)
+ integrate(integrate(-(r^2-1/4)*r,r,0,1/2),theta,0,%pi/4);
expand(%*8);

Result

(%i17) integrate(integrate(sqrt(abs(x-y)),y,0,1),x,0,1);
integrate(integrate(sqrt(x-y),y,0,x),x,0,1)*2;

Result


Created with wxMaxima.