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

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…

Krystian Karczyński

Założyciel i szef serwisu eTrapez.

Magister matematyki Politechniki Poznańskiej. Korepetytor matematyki z wieloletnim stażem. Twórca pierwszych Kursów eTrapez, które zdobyły ogromną popularność wśród studentów w całej Polsce.

Mieszka w Szczecinie. Lubi spacery po lesie, plażowanie i kajaki.

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