Let I_n = ^nx,dx, (n1).

Question

Let $I_n = \displaystyle\int 	an^nx\,dx$, $(n>1)$. $I_4+I_6 = a	an^5x + bx^5 + C$ where C is constant of integration, then the ordered pair $(a,b)$ is equal to:

Accepted Answer

Let $I = I_4+I_6 = \int(	an^4x+	an^6x)\,dx = \int 	an^4x\sec^2x\,dx$

Let $	an x = t \Rightarrow \sec^2x\,dx = dt$

$I = \int t^4\,dt = \dfrac{t^5}{5}+C = \dfrac{1}{5}	an^5x + C$

On comparing: $a = \dfrac15$, $b = 0$

Solutions · 1