$\int e^{x}\sec x\,(1+ an x)\,dx$ equals

Question

$\int e^{x}\sec x\,(1+	an x)\,dx$ equals

Accepted Answer

B. $e^{x}\sec x+C$

1. Expand: $e^{x}(\sec x+\sec x	an x)$.
2. Let $f(x)=\sec x$, then $f'(x)=\sec x	an x$.
3. So the integrand is $e^{x}[f(x)+f'(x)]$, giving $e^{x}f(x)+C$.
4. Result: $e^{x}\sec x+C$.
_Source: NCERT Class 12 Mathematics Ch 7 "Integrals", p.329_

Answer

$e^{x}\cos x+C$

Answer

$e^{x}\sin x+C$

Answer

$e^{x}	an x+C$

$\int e^{x}\sec x\,(1+\tan x)\,dx$ equals