Difficult Distribution Function

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SUMMARY

The forum discussion centers on solving the integral ∫(3/4)x²e^(-x/4)³ dx. The correct solution is established as 1 - e^(-x/4)³. A user expresses difficulty in integrating the function, specifically the term e^(-x/4)³, which is clarified by another participant. The integral can be approached using substitution, specifically u = x³, leading to a more manageable form for integration.

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trojansc82
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Homework Statement


∫3/43x2e-(x/4)3


Homework Equations


F(x) = 0∫xf(t) dt


The Attempt at a Solution



The solution is 1 - e-(x/4)3

I have tried integrating but I am not able to arrive at the solution...

What is the indefinite integral of e-(x/4)3?
 
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trojansc82 said:

Homework Statement


∫3/43x2e-(x/4)3


Homework Equations


F(x) = 0∫xf(t) dt


The Attempt at a Solution



The solution is 1 - e-(x/4)3

I have tried integrating but I am not able to arrive at the solution...

What is the indefinite integral of e-(x/4)3?

It is hard to make out what your equations actually are. But you aren't asked to integrate e-(x/4)3. You have an x2 in there. Basically, ignoring the constants you have an integral of the form

\int x^2e^{-x^3}\, dx

and you need to do a substitution similar to u = x3, du = 3x2dx but modified to include your constants.
 

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