limit integral

lim[n-->oo][ ∫ [0-->oo]-[ (1/n) ] d[x] ] = 1


lim[n-->oo][ ∫ [0-->oo]-[ (1/n)·(x/n)^{m} ] d[x] ] = (1/(m+1))


lim[n-->oo][ ∫ [0-->oo]-[ (1/n)·e^{(1/n)·x} ] d[x] ] = e+(-1)


lim[n-->oo][ ∫ [0-->oo]-[ (1/n)·( 1/( (x/n)+1 ) ) ] d[x] ] = ln(2)


lim[n-->oo][ ∫ [0-->oo]-[ (1/n)·( 1/( (x/n)+a ) ) ] d[x] ] = ln( (1/a)+1 )