Original
Yo Riley, is it just me, or are integrals kind of fun?
{{CMD_7}} I always feel accomplished when I finish one.
{{CMD_8}} I know! Also, even though antiderivatives are difficult,
we can always check our work by taking the derivative.
{{CMD_9}} So awesome!
{{CMD_10}} But something is bothering me. When we are doing substitution,
we have to find {{MATH_11}} and {{MATH_12}} such that
{{MATH_13}}
How do we choose {{MATH_14}} and {{MATH_15}}?
{{CMD_16}} Well, never ever pick {{MATH_17}}, this doesn't change
anything!
{{CMD_18}} And never ever pick {{MATH_19}} to be the entire integrand,
this doesn't help either.
{{CMD_20}} Somehow we must ``see'' one function ``nested'' inside of
another.
{{CMD_21}} I'm not sure there's an easy path to doing, this, I think
it's gonna take practice.
{{CMD_22}}