What? This doesn't make sense. Obviously you have to show work because you can use the wrong techniques to get the right result otherwise and doing that is bad

What? This doesn't make sense. Obviously you have to show work because you can use the wrong techniques to get the right result otherwise and doing that is bad because you won't know why that won't work elsewhere. In high school, we had to know how to rapidly solve questions like integrate e^(ax)•cos(bx) for constants a and b (this is one of those easy ones) and we knew the closed form answer and if we'd forgotten, we'd add an imaginary i•sin(bx), integrate the resulting exponential only and then separate real and imaginaries. But whether that's legal is kinda not obvious. It's just letter manipulation to do that. In a proof, it's for you, so you know you did a legal thing.