The premier of Man versus Calculus Episode 1.

(The comic was in the right track, though it is a tricky substitution. Hold on the substitution and you will have to manipulate with the integral equation. Multiply the numerator and denominator by 2… Watch how the magic works (and I’m still obeying all the math laws)

∫ 2(x + 4) / 2(x^2 + 2x + 5) dx

1/2 ∫ (2x + 8) / (x^2 + 2x + 5) dx

Now, let’s play around with this a little bit. Let’s have some common sense here:

1 + 1 + 1 = 3 is the equivalent as 1 + 2 = 3

With that in mind… 2x + 8 is the same as 2x + 2 + 6, therefore, we can do this:

1/2 ∫ (2x + 2 + 6) / (x^2 + 2x + 5) dx

What’s nice about the addition signs are that one of the fundamental rules of calculus is that as long as there is an + or a - sign, you can split that up into different integrals. In this case, the numerator has the +’s. While we can split them up into three different integrals, it would be more beneficial if we split up the 2x + 2 and the 6. [Because of that substitution the guy left out in the beginning]

1/2 ∫ (2x + 2) / (x^2 + 2x + 5) dx + 1/2 ∫ 6 / (x^2 + 2x + 5) dx

1/2 ∫ 1 / u du + 3 ∫ 1 / (x^2 + 2x + 5) dx

It’s not so bad from there. (But then of course if you’ve never heard of this topic, this is all bad for you. This is the future of what you might do depending on your major! Oooo!~)