Question

$∫e^x secx(1+tanx)dx$ equals

• A. $e^xcosx+C$
• B. $e^xsecx+C$
• C. $e^xsinx+C$
• D. $e^xtanx+C$

Answer 1

Answer: (A)

$e^xcosx+C$

Answer 2

The correct answer isB: $I=e^xsecx+C$
$∫e^x secx(1+tanx)dx$
Let $I=∫e^xsecx(1+tanx)dx=∫e^x(secx+secx\,tanx)dx$
Also,let $secx=ƒ(x)\,\,secx\,tanx=ƒ'(x)$
It is known that,$∫e^x[ƒ(x)+ƒ'(x)]dx=e^xƒ(x)+C$
$∴I=e^xsecx+C$
Hence,the correct answer is B.