How do you integrate #int cos(t^3)#?

Answer 1

It cannot be done in terms of elementary functions . Below you'll see a screenshot of the Wolfram Alpha output. It involves the non-elementary "Gamma function ".

Here's the screenshot with the answer in terms of #Gamma(t)#:

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Answer 2

Ezekiel Alexander

To integrate ( \int \cos(t^3) ), there isn't an elementary antiderivative expressible in terms of standard mathematical functions. This integral involves a special function called the Fresnel integral, denoted as ( \operatorname{FresnelC}(x) ). Therefore, the integral can be expressed as:

[ \int \cos(t^3) , dt = \operatorname{FresnelC}(t) + C ]

Where ( C ) is the constant of integration.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.