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integral (limits ln(2) to ln(4)) [e^(2x)] / [1+e^(2x)] Solution u = 1 + e^(2x) d

ID: 2361073 • Letter: I

Question

integral (limits ln(2) to ln(4)) [e^(2x)] / [1+e^(2x)]

Explanation / Answer

u = 1 + e^(2x) du = 2 * e^(2x) * dx e^(2x) * dx / (1 + e^(2x)) => (1/2) * 2 * e^(2x) * dx / (1 + e^(2x)) => (1/2) * du / u Integrate (1/2) * ln|u| + C => (1/2) * ln|1 + e^(2x)| + C From ln(2) to ln(4) (1/2) * ln|1 + e^(2 * ln(4))| - (1/2) * ln|1 + e^(2 * ln(2))| => (1/2) * ln|1 + e^ln(16)| - (1/2) * ln|1 + e^ln(4)| => (1/2) * ln|1 + 16| - (1/2) * ln|1 + 4| => (1/2) * ln(17) - (1/2) * ln(5) => (1/2) * (ln(17) - ln(5)) => (1/2) * ln(17/5) link: http://answers.yahoo.com/question/index;_ylt=AuojUtwlM5ufCdHw74AAkZoCxgt.;_ylv=3?qid=20121214135850AALgsKp

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