Integration by Parts homework assistance

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Homework Help Overview

The problem involves the integration of the function ∫x³e^(5x²) dx, which falls under the subject area of calculus, specifically focusing on integration techniques such as integration by parts.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the setup for integration by parts, with one suggesting to express the integral in a specific form to facilitate the process. There are attempts to define variables for integration and to apply the integration by parts formula.

Discussion Status

The discussion has seen participants sharing their attempts and reasoning. One participant expresses initial confusion but later indicates progress in understanding the problem. There is no explicit consensus, but guidance has been provided in the form of hints and variable definitions.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the extent of assistance they can provide to one another.

AryRezvani
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Homework Statement



∫x3e5x2 dx

Homework Equations



uv-∫vdv

The Attempt at a Solution



I've tried this one a few times, but keep getting answers that are just out there. Could someone, if possible, work out just the beginning.
 
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AryRezvani said:

Homework Statement



∫x3e5x2 dx

Homework Equations



uv-∫vdv

The Attempt at a Solution



I've tried this one a few times, but keep getting answers that are just out there. Could someone, if possible, work out just the beginning.

OK, just one hint to get you started. You should start by expressing the problem as:

\int (x^2).(xe^{5x^2})dx
 
Hmm okay, got it.

So let's say U = x2
dU = 2x

dv = xe5x2
V=1/10e5x2

Then, plug into the equation, and you get...

(x2)(1/10e5x2) - ∫(1/10e5x2)2x dx

EDIT: Just got it, thanks a lot for your time :).
 
Last edited:
AryRezvani said:
Hmm okay, got it.

So let's say U = x2
dU = 2x

dv = xe5x2
V=1/10e5x2

Then, plug into the equation, and you get...

(x2)(1/10e5x2) - ∫(1/10e5x2)2x dx

EDIT: Just got it, thanks a lot for your time :).
No worries. :smile:
 

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