Better way of saying "in order to demonstrate this"
Solution 1:
Perhaps "To illustrate this, I will...", "Demonstrating this, I will..." or "As an example,.."
Solution 2:
I would sometimes use "to this end", however that is also more a general term. Something like: "We wish to show that space whales are secretly communicating with us. To this end, we will monitor the frequencies determined to be most likely to carry space whale song."