Question

find the value of (slv ths)​

Answer 1

$\underline{\large{\sf Answer:}}$

$\sf \int{e^x(tanx+sec^2x)}dx$

here we have ,

tanx and sec²x, let us consider,

y = tanx , i.e f(x)=tanx

Differentiate wrt t

dy/dx = sec²x = f'(x)=sec²x

We know, integral of the form

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

therefore ,

$\sf \int{e^x(tanx+sec^2x)}dx$

$\sf = e^x . f(x) + c$

$\boxed{\sf I = e^x.tanx + c}$