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Determine the integral $\int \dfrac{e^x+\sec^2x}{e^x+\tan x}           dx$
in MAT1581 by Diamond (41.3k points) | 27 views

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let $u=e^x+\tan x$

$\dfrac{du}{dx}=e^x+\sec^2x$

$du=(e^x+\sec^2x)dx$

$dx=\dfrac{du}{e^x+\sec^2x}$

$\int \dfrac{e^x+\sec^2x}{u} *\dfrac{du}{e^x+\sec^2x}$

$\int \dfrac{1}{u}du$

$ln u + c$

$ln (e^x+\tan x) + c $
by Wooden (3.5k points)
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