aprilanahi
Find the indefinite integral of (y+(2/sin^2y))dy



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JamesJ
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Hint: what's the derivative with respect to y of cot(y) ?

aprilanahi
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cscx?

JamesJ
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No. But it is related to the 1/sin^2 y in your question

aprilanahi
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I still don't get it?

aprilanahi
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csc^2x

JamesJ
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\[ \frac{d }{dy} \cot y =  \frac{1}{\sin^2 y} =  \csc^2 y \]

JamesJ
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Hence
\[ \int \left( y + \frac{2}{\sin^2 y} \right) \ dy = \int y \ dy + 2 \int \csc^2 y \ dy = ... \]

aprilanahi
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So what's the answer?

JamesJ
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You tell me. I've done the first few steps for you. You only have 2 more to do: evaluate each of those integrals above

aprilanahi
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y^2/2+2cotx+c

JamesJ
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Double check your signs!

aprilanahi
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Negative cotx

JamesJ
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yes

aprilanahi
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Yes, thank you!!!