Question

$$ \int_{-2} \frac{e^{17z}}{e^{17z}+1} dz $$ $$ u = e^{17z}+1 $$ $$ du = e^{17z} \cdot 17 dz $$ $$ \frac{1}{17} du = e^{17z} dz $$ $$ = \int \frac{\frac{1}{17} du}{u} $$ $$ = \frac{1}{17} \int_{e^{-34}+1}^{e^{34}+1} \frac{du}{u} $$ $$ = \frac{1}{17} \ln|u| \Big|_{e^{-34}+1}^{e^{34}+1} $$ $$ = \frac{1}{17} (\ln(e^{34}+1) - \ln(e^{-34}+1)) $$

Name: int 2 frace17ze17z1 dz u e17z1 du e17z cdot 17 dz frac117 du e17z dz int fracfrac117 duu frac117 inte 341e341 fracduu frac117 lnu bige 341e341 frac117 lne341 lne 341 53565
Uploaded: 2020-05-23T03:55:50-08:00
Duration: 1 min 23 s
Channel: Amy Jiang
Description: int 2 frace17ze17z1 dz u e17z1 du e17z cdot 17 dz frac117 du e17z dz int fracfrac117 duu frac117 inte 341e341 fracduu frac117 lnu bige 341e341 frac117 lne341 lne 341 53565

          $$ \int_{-2} \frac{e^{17z}}{e^{17z}+1} dz $$
$$ u = e^{17z}+1 $$
$$ du = e^{17z} \cdot 17 dz $$
$$ \frac{1}{17} du = e^{17z} dz $$
$$ = \int \frac{\frac{1}{17} du}{u} $$
$$ = \frac{1}{17} \int_{e^{-34}+1}^{e^{34}+1} \frac{du}{u} $$
$$ = \frac{1}{17} \ln|u| \Big|_{e^{-34}+1}^{e^{34}+1} $$
$$ = \frac{1}{17} (\ln(e^{34}+1) - \ln(e^{-34}+1)) $$

$int 2 frace17ze17z1 dz u e17z1 du e17z cdot 17 dz frac117 du e17z dz int fracfrac117 duu frac117 inte 341e341 fracduu frac117 lnu bige 341e341 frac117 lne341 lne 341 53565$

Added by Gina H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Amy Jiang

05/23/2020

Step 1

The given integral is $$ \int_{-2} \frac{e^{17z}}{e^{17z}+1} dz $$. It appears the lower limit of integration is -2, but the upper limit is missing. However, the subsequent steps show definite integral evaluation with limits derived from z=-2 and z=2. Assuming the Show more…

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$$ \int_{-2} \frac{e^{17z}}{e^{17z}+1} dz $$ $$ u = e^{17z}+1 $$ $$ du = e^{17z} \cdot 17 dz $$ $$ \frac{1}{17} du = e^{17z} dz $$ $$ = \int \frac{\frac{1}{17} du}{u} $$ $$ = \frac{1}{17} \int_{e^{-34}+1}^{e^{34}+1} \frac{du}{u} $$ $$ = \frac{1}{17} \ln|u| \Big|_{e^{-34}+1}^{e^{34}+1} $$ $$ = \frac{1}{17} (\ln(e^{34}+1) - \ln(e^{-34}+1)) $$