Question

Find the following integral : $\int sec\ x(sec\ x+tan\ x) \, dx$

Answer 1

Answer:

Step-by-step explanation:

Concept:

$1.\int[f(x)+g(x)]\:dx=\int{f(x)}\;dx+\int{g(x)}\;dx\\\\2.\int{secx.tanx}\:dx=secx+c\\\\3.\int{sec^2x}\:dx=tanx+c$

Now,

$\int{secx(secx+tanx)}\:dx\\\\=\int[sec^2x+secx\;tanx]\:dx\\\\=\int{sec^2x}\:dx+\int{secx\;tanx}\:dx\\\\\=tanx + secx + c$