Gujarat Boardગુજરાતી માધ્યમધોરણ 12 સાયન્સગણિતસંકલન1 Mark
MCQ
$I=\int e^x \sec x(1+\tan x) d x=\ ...... $
A
$e^x \cos x + c$
✓
$e^x \sec x + c$
C
$e^x \sin x + c$
D
$e^x \tan x + c$
✓
Answer
Correct option: B.
$e^x \sec x + c$
$I=\int e^x \sec x(1+\tan x) d x $
$=\int e^x(\sec x+\sec x \tan x) d x$
$f(x)=\sec x $ હોય તો $f^{\prime}(x)=\sec x \tan x $ થાય.
$\int e^x\left(f(x)+f^{\prime}(x)\right) d x=e^x f(x)+c$
$I=e^x \sec x+c$
$\therefore$ વિકલ્પ $(B)$ આવે.
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