S3 to infinity 12x113 dxSolution12x11312x13 take 2xt hence

S(3 to + infinity) 1/(2x-1)^1/3 dx

1/(2x-1)^(1/3)>1/(2x)^1/3

take

2x=t

hence our imit are from

6<t<infinity

then

1/(t-1)^(1/3)>1/t^(1/3)

since

1/t^(1/3) is divergent

and

it is always smaller then

1/(t-1)^(1/3)

on the given interval

hence

1/(t-1)^(1/3)

is divergent

and so

1/(2x-1)^(1/3)

is divergent