Question

Integrate of ex sec x(1+tanx) dx

Answer 1

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

$=\int\,e^x(sec\,x+sec\,x\,tan\,x)\,dx$

$\boxed{\begin{minipage}{4cm}\text{Take } f(x)=sec\,x\\\\ \text{Then, } f'(x)=sec\,x\,tan\,x \end{minipage}}$

$=\int\,e^x[(f(x)+f'(x)]\,dx$

$\text{Using the following result }$

$\boxed{\bf\,\int\,e^x[(f(x)+f'(x)]\,dx=e^x\,f(x)+c}$

$=\,e^x\,f(x)+c$

$=\,e^x\,secx+c$

$\therefore\bf\int\,e^x\,sec\,x(1+tan\,x)\,dx=\,e^x\,secx+c$

Answer 2

Step-by-step explanation:

hope it will help u dude