INTEGRATION ( a das - D-134)

\sec x +\tan x =t \\ \\ \\ \frac{dt}{t}=\sec x .dx\\ \\ \\ \int \frac{\sec x .dx }{(\sec x + \tan x)^n}=\int {t^{-n-1}dt}=\frac{-1}{nt^n}=-\frac{1}{n(\sec x + \tan x)^n} \\ \\ \\ \int_{0}^{\frac{\pi}{2}}{\sec x \frac{\sec x .dx }{(\sec x + \tan x)^n}}= \frac{-\cos ^ {n-1}x}{n(1 + \sin x )^n}|_0^{\frac{\pi}{2}}+\underline {\int_{0}^{\frac{\pi}{2}}{\sec x \tan x\frac{1}{n(\sec x + \tan x)^n}}}\\ \\ \\ \\ \text{now to evaluate this take tan as first function , then u will agin get I(n), which gives the answer }