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What squared equals 17? Namely, indefinite integrals and the formula with arctan

Krystian Karczyński

Founder and General Manager of eTrapez.

Graduate of Mathematics at Poznan University of Technology. Mathematics tutor with many years of experience. Creator of the first eTrapez Courses, which have gained immense popularity among students nationwide.

He lives in Szczecin, Poland. He enjoys walks in the woods, beaches and kayaking.


The arctan Formula in Typical Indefinite Integrals

We’ve gotten used to using this formula: in “pure” integral situations,

such as:

Then we simply transform…

…and elegantly arrive at the result:

The arctan Formula in Atypical Situations in Indefinite Integrals

And what about this indefinite integral:

? What squared equals 17? Nothing? Nope… squared equals 17, so:

Generally speaking, the formula will handle any indefinite integral of this type, constants in the denominator may not be so easy to represent as a square…


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