While increasing aspect ratio is commonly used to reduce induced drag, it must be remembered that induced drag is fundamentally not a function of aspect ratio, but of wingspan. Induced drag is inversely proportional the the square of the wingspan. Increasing wingspan by 10% will reduce induced drag by 19%, regardless of what you do the the wing chord at the same time. It took me a while to get my head around this too, but I found that the concept of span loading considerably simplified drag calculations.

For the same span and lift, a wing of aspect ratio 4 will have the same induced drag as one with aspect ratio 20 as long as the wing is unstalled, but its total drag will be far higher, simply because it has much more form drag and skin friction. Total wing drag is minimized by using the maximum practical span, along with the minimum chord required to obtain enough wing area to keep the wing just a bit below the lift coefficient at which stall burbles begin to increase drag.