If
In=tannx‌dx, for
n≥2, then
In+In−2= We can solve this problem using integration by parts. Let's start by writing out the integral for
In :
We can then use the identity
tan2x=sec2x−1 to rewrite the integral as:
Let's focus on the first integral. We can use u-substitution with
u=tan‌x and
du=sec2x‌dx :
The second integral is simply
In−2. Therefore, we can write:
In=‌−In−2Rearranging this equation, we get:
In+In−2=‌So the answer is Option A.