Is Integration by Parts Incorrect for ∫(x2 + 7x) cosx dx?

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Discussion Overview

The discussion revolves around the application of integration by parts to the integral ∫(x² + 7x) cos(x) dx. Participants explore different approaches to the integration process and express confusion regarding the correctness of their methods.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant proposes using integration by parts with v = (x² + 7x) and du = cos(x) dx, resulting in an expression that they believe is incorrect.
  • Another participant asserts that the integration by parts is being applied incorrectly without providing specific corrections.
  • A different participant suggests expanding the integrand into two separate terms, x² cos(x) and 7x cos(x), and recommends integrating the second term first.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the integration by parts application. Multiple competing views on the approach remain, and the discussion is unresolved regarding the best method to solve the integral.

Contextual Notes

There are limitations in the discussion regarding the assumptions made in the integration by parts process and the potential need for further clarification on the steps involved in the integration.

loserspearl
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∫(x2 + 7x) cosx dx

If I make v = (x2 + 7x) and du = cosx dx I get
((x2 + 7x) sinx)/2

If I make v = cosx and du = (x2 + 7x) dx I get
((x3/3 + 7x2/2) cosx)/2

using the form X=Y-X to X=Y/2

Neither are correct, what did I do wrong?
 
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Integration by parts:
∫u dv = uv - ∫v du

You are doing the integration by parts incorrectly.
 
Last edited:
loserspearl said:
∫(x2 + 7x) cosx dx

If I make v = (x2 + 7x) and du = cosx dx I get
((x2 + 7x) sinx)/2

If I make v = cosx and du = (x2 + 7x) dx I get
((x3/3 + 7x2/2) cosx)/2

using the form X=Y-X to X=Y/2

Neither are correct, what did I do wrong?

I recommend you expand the integrand (x2 + 7x) cosx into x2 cos x + 7x cos x, and integrate the two resulting terms.
I would start with integrating the second term of this expansion first.
 
K thanks
 

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