積分關於8/(x^2+16)?

2012-01-01 10:21 am
積分關於8/(x^2+16)?

步驟和let u唔該。

回答 (1)

2012-01-01 9:40 pm
✔ 最佳答案
This question should be applied by trigonometric substitution.
Let x = 4 tan θ => dx = 4 sec^2 θ dθ
∫8/(x^2 + 16) dx
= (8/16)∫1/sec^2 θ (4 sec^2 θ dθ)
= 2∫dθ
= 2θ + C
= 2(tan^-1 x/4) + C
參考: Knowledge is power.


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