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Income Taxes (Reconciliation of U.S Statutory Rate to Effective Tax Rate) (Details)
12 Months Ended
Sep. 30, 2017
Sep. 30, 2016
Sep. 30, 2015
Income Taxes      
Statutory tax rate 35.00% 35.00% 35.00%
State income taxes, net of federal tax benefit (0.30%) 0.40% 1.20%
Taxes on international activities (7.60%) (2.20%) (3.80%)
Research credit (3.20%) (3.60%) (0.80%)
Retroactive extension of research credit   (3.20%) (2.40%)
Net excess income tax benefit from stock-based compensation (1.40%) (2.60%)  
Domestic production activities deduction (1.50%) (2.10%) (1.60%)
Adjustments of prior period tax items (0.90%) (0.20%) (2.10%)
Other items, net 0.60% (1.30%) (0.80%)
Effective tax rate 20.70% 20.20% 24.70%