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Answer:
f(x) = secx
Step-by-step explanation:
[tex]\int\limits {e^x(tanx+1)secx}\,dx[/tex]
= [tex]\int\limits {e^x(tanxsecx+secx)}\,dx[/tex]
= [tex]\int\limits {(e^xtanxsecx+e^x secx)}\,dx[/tex] ............................(i)
Let,
[tex]e^xsecx = y[/tex]
[tex](e^xsecx + e^x secx \times tanx )dx= dy[/tex]
Now, (i) ............
= [tex]\int\limits dy[/tex]
= y + c
= [tex]e^xsecx[/tex] + c = [tex]e^x f(x) +c[/tex]
So, f(x) = secx
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