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Aaron Coleman 2022-04-30 Answered
What is 2 9  4 x + 5 d x?
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Answers (1)

zavesiljid
Answered 2022-05-01 Author has 21 answers
Since 2 9 is constant with respect to x, move 2 9 out of the integral.
2 9 4 x + 5 d x
Let u=4x+5. Then du=4dx, so 1 4 d u = d x. Rewrite using u and du.
2 9 u 1 4 d u
Combine u and 1 4 .
2 9 u 4 d u
Since 1 4 is constant with respect to u, move 1 4 out of the integral.
2 9 ( 1 4 u d u )
Simplify the expression.
1 18 u 1 2 d u
By the Power Rule, the integral of u 1 2 with respect to u is 2 3 u 3 2
1 18 ( 2 3 u 3 2 + C )
Simplify
1 27 u 3 2 + C
Replace all occurrences of u with 4x+5.
1 27 ( 4 x + 5 ) 3 2 + C
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