The title is overoptimistic. This only work if you have a good understanding of the of the function to have a good enough guess of the integral.
There are many integration methods that use guess or try to explote the similarity of the integral with the integral of a simpler function. Relevant xkcd: https://xkcd.com/2117/
In particular, this method use some intuitive version of substitutions, i.e. the integral of f(3x+5) is somewhat similar to g(3x+5), for any 3x+5 out there. I strongly recommend to study the usual substitution method to get enough enlightenment.
Integration by parts is more tricky. It is useful in a lot of elemental cases, and has a lot of applications in advanced mathematic and physics, but I still didn't reach the enlightenment phase.
You can try to ignore integration by parts if it's not in the midterm, but substitution is too important to be ignored.
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[ 3.5 ms ] story [ 15.2 ms ] threadThere are many integration methods that use guess or try to explote the similarity of the integral with the integral of a simpler function. Relevant xkcd: https://xkcd.com/2117/
In particular, this method use some intuitive version of substitutions, i.e. the integral of f(3x+5) is somewhat similar to g(3x+5), for any 3x+5 out there. I strongly recommend to study the usual substitution method to get enough enlightenment.
Integration by parts is more tricky. It is useful in a lot of elemental cases, and has a lot of applications in advanced mathematic and physics, but I still didn't reach the enlightenment phase.
You can try to ignore integration by parts if it's not in the midterm, but substitution is too important to be ignored.