Integration: Exercise 3
About the Lecture
The lecture Integration: Exercise 3 by Batool Akmal is from the course Advanced Integration.
Included Quiz Questions
To evaluate the integral ∫ x/(2x + 1)² dx using the integration by parts method, how should u and v' be chosen?
- u = x and v' = (2x + 1)⁻²
- u = x(2x + 1)⁻¹ and v' = (2x + 1)⁻¹
- u = (2x + 1)⁻² and v' = x
- u = (2x + 1)⁻¹ and v' = x(2x + 1)⁻¹
- u = x(2x + 1)⁻² and v' = 1
What is the evaluation of the integral ∫x/(2x+1)²dx ? Use integration by parts.
- (1/4)ln|2x + 1| - x / (4x + 2) + c
- (1/2)ln|2x + 1| - x/(2x + 1) + c
- (-1/4)ln|2x + 1| + x / (4x + 2) + c
- ln|2x + 1| - x / (2x + 1) + c
- (1/2)ln(2x + 1) - x / (2x + 1) + c
What is the evaluation of the indefinite integral ∫2x/(x + 1)⁴ dx ? Use integration by parts.
- (-1/3) / (x + 1)² - (2/3)x/(x + 1)³ + c
- (-1/3) / (x + 1) - (1/3)x/(x + 1)³ + c
- (+1/3) / (x + 1)² + (2/3)x/(x + 1)³ + c
- (+1/3) / (x + 1) + (1/3)x/(x + 1)³ + c
- (-1/3)x / (x + 1)² - (2/3)/(x + 1)³ + c
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Author of lecture Integration: Exercise 3
Batool Akmal
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