CAPT OF AN LTT FAILED TO HOLD SHORT OF A RWY DURING TAXI FOR TKOF.

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AT MDW WHILE TAXIING FROM THE END OF CONCOURSE B (OUR PARKING SPOT) TO RWY 31C VIA TXWYS P AND G; WE APPARENTLY CROSSED RWY 31R WITHOUT CLRNC. AFTER WE CROSSED IT; GND TOLD US THAT WE WERE SUPPOSED TO HAVE HELD SHORT OF RWY 31R; BUT 'NO PROB THIS TIME.' HOW DID THIS HAPPEN? ALL I REMEMBER HEARING THEM TELL US WAS TO TAXI TO RWY 31C VIA TXWYS P AND G. THE TWR XMISSIONS AT MDW ARE OF A LESS THAN CLEAR QUALITY. THEY ALWAYS SOUND LIKE THEY ARE IN AN ECHO CHAMBER. ALSO; ON THE INBOUND ATIS; I REMEMBER HEARING THAT RWY 31R AND RWY 31L WERE CLOSED; SO PERHAPS I DIDN'T PAY CLOSE ATTN TO THE TAXI INSTRUCTIONS BECAUSE I ASSUMED THE OTHER RWYS WERE CLOSED. OF COURSE; WE WERE ALSO RUNNING OUR CHKLISTS AND LISTENING TO GND AT THE SAME TIME. FURTHER; I WAS RUSHING; WE WERE A TAD LATE AND AN ACFT SPD RESTR WOULD CAUSE US TO BE LATER YET. AND LAST; BUT NOT LEAST; THIS WAS THE LAST LEG OF BASICALLY A 5 DAY TRIP FOR ME (A 2 DAY TRIP; FOLLOWED IMMEDIATELY BY A 3 DAY). OVER THE 5 DAYS; I FLEW 23 LEGS; 26.5 HRS; ENCOUNTERED NUMEROUS FRUSTRATIONS DUE TO WX AND MAINT/MECHANICAL PROBS. I WAS PROBABLY MORE FATIGUED THAN I REALIZED. LESSON LEARNED: SLOW DOWN; DON'T RUSH; CONFIRM RWY XINGS!