Integrate cos x / (5+2 sin x) dx
I am very confused. Help me.
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Plz answer this but I need the explanation completely?
2016-06-20 10:19 pm
回答 (3)
2016-06-20 10:26 pm
✔ 最佳答案
Let u = 5 +2sinxThen du = 2 cosx dx
Then integrate (1/2) du / u = (1/2)ln|u| + C =
(1/2)ln|5 + 2sinx| + C
2016-06-20 10:26 pm
Let u = 5 + 2 sin x
Then, du = -2 cos x dx
∫[cos x / (5 + 2 sin x)] dx
= ∫[1 / (5 + 2 sin x)] [cosx dx]
= ∫[1 / (5 + 2 sin x)] (-1/2) [-2 cosx dx]
= (-1/2) ∫[1 / (5 + 2 sin x)] [-2 cosx dx]
= (-1/2) ∫[1 / u] du
= (-1/2) ln|u| + C
= (-1/2) ln|5 + 2 sin x| + C
Then, du = -2 cos x dx
∫[cos x / (5 + 2 sin x)] dx
= ∫[1 / (5 + 2 sin x)] [cosx dx]
= ∫[1 / (5 + 2 sin x)] (-1/2) [-2 cosx dx]
= (-1/2) ∫[1 / (5 + 2 sin x)] [-2 cosx dx]
= (-1/2) ∫[1 / u] du
= (-1/2) ln|u| + C
= (-1/2) ln|5 + 2 sin x| + C
2016-06-20 10:26 pm
Integrate cos x / (5+2 sin x) dx , u = 5+2 sin x
=(1/2) ln(5+2 sin x)+C
=(1/2) ln(5+2 sin x)+C
收錄日期: 2021-04-18 15:14:44
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