Antiderivative of some functions

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Homework Help Overview

The discussion revolves around finding the antiderivatives of specific functions, including cos(t^5), tan(x^2), and (1-x^2)^(1/3). The subject area is calculus, particularly focusing on integration and antiderivatives.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the functions, with one noting that none of them are elementary functions. Others suggest using computational tools like Maple or Mathematica for assistance.

Discussion Status

The conversation is ongoing, with participants exploring the complexity of the functions and considering the use of software for integration. There is no explicit consensus on how to approach the antiderivatives, but guidance towards computational resources has been provided.

Contextual Notes

Participants are operating under the assumption that the functions in question do not have elementary antiderivatives, which influences the direction of the discussion.

JinSu
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Anyone know how to get antiderivative of these? I am stuck.

1) cos(t^5)
2) tan(x^2)
3) (1-x^2)^(1/3)

Any explanation on how to do these would be appreciated.
 
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None of them are elementary functions.
 
int cost^5 = 1/11*t*(5*sin(t^5)*t^5*(t^5)^(7/10)+11*(t^5)^(7/10)*cos(t^5)-5*t^5*sin(t^5)*LommelS1(17/10, 3/2, t^5)-11*t^5*LommelS1(7/10, 1/2, t^5)*cos(t^5)+11*LommelS1(7/10, 1/2, t^5)*sin(t^5))/(t^5)^(7/10)
 

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