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Find the integral of (2x + 1)^3 dx. (2019)
Find the integral of (2x + 1)^3 dx. (2019)
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Practice Questions
1 question
Q1
Find the integral of (2x + 1)^3 dx. (2019)
(1/4)(2x + 1)^4 + C
(1/3)(2x + 1)^4 + C
(1/5)(2x + 1)^4 + C
(1/2)(2x + 1)^4 + C
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Using substitution, the integral is (1/4)(2x + 1)^4 + C.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the integral of (2x + 1)^3 dx. (2019)
Solution:
Using substitution, the integral is (1/4)(2x + 1)^4 + C.
Steps: 9
Show Steps
Step 1: Identify the integral you need to solve: ∫(2x + 1)³ dx.
Step 2: Use substitution. Let u = 2x + 1. This means that du/dx = 2, or du = 2 dx.
Step 3: Solve for dx in terms of du: dx = du/2.
Step 4: Substitute u and dx into the integral: ∫(u)³ (du/2).
Step 5: Factor out the 1/2: (1/2) ∫u³ du.
Step 6: Now, integrate u³: ∫u³ du = (1/4)u⁴ + C.
Step 7: Combine the results: (1/2) * (1/4)u⁴ + C = (1/8)u⁴ + C.
Step 8: Substitute back u = 2x + 1: (1/8)(2x + 1)⁴ + C.
Step 9: Simplify the expression: (1/4)(2x + 1)⁴ + C.
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