Even though your capital gains are reported on line 13 of your form 1040, those gains are not taxed as ordinary income.
Line 44 of your form 1040 is where you enter the amount of tax that you owe. Please note that the instructions for line 44 tell you that if part of your taxable income is from capital gains, you need to complete the worksheet contained in the instructions for Schedule D to calculate your tax. You cannot simply use the tax tables. If you would just use the tax tables, you are correct that those gains would be taxed as ordinary income.
By using the worksheet contained in Schedule D to calculate the taxes you owe, it will properly tax the long term capital gains at 15% and the rest of your income at ordinary rates. You then enter the tax figure from that worksheet on line 44 of your form 1040.
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Thank you John