Question

integration sec4xtanx dx​

Answer 1

Answer:

$\bf{\int{sec^4x\:tanx\:dx​=\frac{sec^4}{4}+c}$

Explanation:

I have applied change of variable method to solve this problem

$I=\int{sec^4x\:tanx}\:dx$

$I=\int{sec^3x(secx\:tanx)\:dx$

Take

$t=secx$

$\frac{dt}{dx}=secx\:tanx$

$dt=secx\:tanx\:dx$

Now,

$I=\int{t^3}\:dt$

$I=\frac{t^4}{4}+c$

$\implies\:\bf{I=\frac{sec^4}{4}+c}$