bmelyk
Find the indefinite integral:



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bmelyk
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\[\int\limits_{?}^{?}\frac{ e^{y} }{ 2e^{y} } dy\]

bmelyk
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i know i'll be using substitution.

TuringTest
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Let\[u=2e^y\]then\[du=?\]

bmelyk
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e^y y dy?

TuringTest
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\[u=2e^y\implies du=e^ydy\implies e^ydy=du\]so what is the integral now?

bmelyk
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\[\int\limits_{?}^{?} 1/du du\]

bmelyk
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well minus?

TuringTest
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how did you get two du's ?

bmelyk
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\[\int\limits_{e^y}}^{2e^{y}} e^{\]

bmelyk
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\[\int\limits_{}^{} \frac{ e^{y} }{ 2e{y} } e^{y}\]

TuringTest
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where is the other e^y coming from?

bmelyk
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thats my du.

bmelyk
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well dy.

bmelyk
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it should be negative.

bmelyk
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is the answer ln2e^y+c?

TuringTest
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you dropped the negative sign, but aside from that the answer is correct