ctmusicgirl7
∫eˣ cot²(eˣ+1) dx. So far, I’ve put u = eˣ + 1 and du = eˣdx and substituted them in, so now I have ∫cot²u du. I’m not sure what to do next, since I can’t figure out the antiderivative for this!
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abb0t
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\[\cot^2(u) = \csc^2(u)-1\]
Both of which are easily integrable.
ctmusicgirl7
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so then i have ∫ (csc²u – 1) du?
abb0t
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Correct.
ctmusicgirl7
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the antiderivative of csc^2 u -1 = -cot u - u?
abb0t
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Correct again.
gerryliyana
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yes
ctmusicgirl7
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thank you! is there some kind of thing on here where i give you points or something for helpuing me :D
abb0t
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Remember to plug u back in to the final answer and add the constant.
oldrin.bataku
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@ctmusicgirl7 click "Best Response"