`A=inte^xsinxdx` and `B=inte^xcosx dx, lim_(x->-oo)A=0,lim_(x->-oo)B=0` then `A^2+B^2` is equal to

A=int e^(x)sin xdx and B=int e^(x)cos xdx,quad lim_(x rarr-oo)A=0,quad lim_(x rarr-oo)B=0 then A^(2)+B^(2) is equal to

If a=lim_(x->oo) sinx/x & b=lim_(x->0) sinx/x Then int (ab log(1+x)+x^2)dx is equal to

lim_(x to oo) ((x+a)/(x+b))^(x+b) is equal to

If lim_(x rarr oo)((x^(2)+x+1)/(x+1)-ax-b)=4 " then a & b is equal to"

lim_(xto oo) (int_(0)^(x)tan^(-1)dt)/(sqrt(x^(2)+1)) is equal to

lim_(x to oo)(int_0^(2x) te^(t^(2))dt)/(e^(4x^(2))) equals

lim_(x rarr oo)(sqrt(x^(2)-x+1)-ax-b)=0, then a+b=

lf lim_(x to 0) (sin x)/( tan 3x) =a, lim_( x to oo) (sinx)/x =b , lim_( x to oo)( log x)/x = c then value of a + b + c is