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ctmusicgirl7

  • 2 years ago

∫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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  1. abb0t
    • 2 years ago
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    \[\cot^2(u) = \csc^2(u)-1\] Both of which are easily integrable.

  2. ctmusicgirl7
    • 2 years ago
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    so then i have ∫ (csc²u – 1) du?

  3. abb0t
    • 2 years ago
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    Correct.

  4. ctmusicgirl7
    • 2 years ago
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    the antiderivative of csc^2 u -1 = -cot u - u?

  5. abb0t
    • 2 years ago
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    Correct again.

  6. gerryliyana
    • 2 years ago
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    yes

  7. ctmusicgirl7
    • 2 years ago
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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

  8. abb0t
    • 2 years ago
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    Remember to plug u back in to the final answer and add the constant.

  9. oldrin.bataku
    • 2 years ago
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    @ctmusicgirl7 click "Best Response"

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