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junior college 1 | H2 Maths
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Hii can u help me with the last part of this qns pls?? Thanku!!!
Date Posted: 3 years ago
Views: 504
Separate the terms first.
∫ (x² + x)/(x² + 9)² dx
= ∫ x²/(x² + 9)² dx + ∫ x/(x² + 9)² dx
Notice that the first term can be integrated using the result you have obtained in the first part. (Follow Tham KY's working in the earlier post)
The second term is directly integrable :
∫ x/(x² + 9)² dx
= ½∫ 2x(x² + 9)⁻² dx
= ½ (-(x² + 9)⁻¹)
= -1/[2(x² + 9)]
(No need to + c since we have a definite integral)
You can try differentiating it to get back the original expression
∫ (x² + x)/(x² + 9)² dx
= ∫ x²/(x² + 9)² dx + ∫ x/(x² + 9)² dx
Notice that the first term can be integrated using the result you have obtained in the first part. (Follow Tham KY's working in the earlier post)
The second term is directly integrable :
∫ x/(x² + 9)² dx
= ½∫ 2x(x² + 9)⁻² dx
= ½ (-(x² + 9)⁻¹)
= -1/[2(x² + 9)]
(No need to + c since we have a definite integral)
You can try differentiating it to get back the original expression
See 1 Answer
See main comments for explanation.
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