E.I. du Pont de Nemours & Co. said it earned $1.08 billion ($5.81 a share) in 1981, a 45 percent increase over 1980 results that was due almost entirely to the addition of net income from Conoco Inc. for the last five months of the year, following its merger with Du Pont on Aug. 1.

Sales increased by $9.1 billion last year to $22.8 billion, with $8.1 billion of the increase contributed by Conoco following the Aug. 1 merger. Conoco's share of Du Pont's net income for 1981 was $316 million after accounting adjustments relating to the merger.

A severe slump in chemical sales, which make up 10 percent of the business of the combined companies, pulled down profits in the fourth quarter of 1981--the first three-month reporting period in which Conoco's and Du Pont's financial data were combined.

Du Pont's fourth-quarter net income was $328 million ($1.35) compared with $215 million ($1.36) in the final quarter of 1980, reflecting the increase in Du Pont shares following the merger.

Fourth-quarter 1981 sales following the merger totaled $8.44 billion, with $5 billion coming from Conoco. Du Pont's sales in the final quarter of 1980 totaled $3.53 billion.

Conoco's income and earnings for the full year were not reported because of complex accounting adjustments required to put both companies on a comparable accounting basis. The $1.08 billion earnings figure does not include $321 million ($1.74 per share) in income due to the change in the accounting treatment of investment tax credits.

Boeing Co., suffering from a severe slump in the airline industry, reported yesterday that its net income last year declined to $473 million ($4.90 a share) from $600.5 million ($6.23) in 1980.

Boeing said profits also were hurt by continuing heavy expenses for its two new aircraft, the 757 and 767 jetliners, that will start being delivered to carriers in the next couple of years.

The company posted a modest rise in total 1981 sales to $9.79 billion from $9.43 billion.

And Celanese Corp., another chemicals, plastics and fiber manufacturer, earned $144 million ($9.01 a share) on sales of $3.8 billion last year, up from earnings of $122 million ($8.20) in 1980 and sales of $3.3 billion.

However its fourth-quarter profit last year was down 17 percent from the final three months of 1980. Fourth-quarter 1981 sales were $884 million, down from $913 million in the same period the year before.