Question

find f(x).…............

Answer 1

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find f(x) :-

In Attachment

$\huge\red{\underline{{\boxed{\textbf{ANSWER}}}}}$

∫e^x(tanx+1)secx

=∫e^x(secx.tanx + secx)

it is of form

∫e^x(f(x) + f'(x))

=e^x.f(x) + C

here, f(x) = secx

hence,

I = e^x.f(x) + C

= e^xsecx + C

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OR:-

e^x[f(x)+f '(x)]=e^xf(x)

So,

e^x(secx*tanx + secx)=e^x secx

as d/dx of secx =secx *tanx

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HARSH PRATAP SINGH

Answer 2

$\huge\underline\bold\blue{ƛƝƧƜЄƦ}$

∫e^x(tanx+1)secx

=∫e^x(secx.tanx + secx)

it is of form

∫e^x(f(x) + f'(x))

=e^x.f(x) + C

here, f(x) = secx

hence,

I = e^x.f(x) + C

= e^xsecx + C