What is the Integral of 3x (sinx/cos^4x) dx?

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Discussion Overview

The discussion revolves around evaluating the integral of the function 3x (sinx/cos^4x) dx. Participants explore methods of integration, particularly focusing on integration by parts.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks for help with the integral of 3x (sinx/cos^4x) dx.
  • Another participant rewrites the integral as 3∫ x tan x sec^3 x dx and suggests using integration by parts.
  • A different participant seeks clarification on the variables used in the integration by parts formula, noting the presence of three different variables.
  • One participant proposes setting u = x and dv = tan x sec^3 x dx, indicating that further integration by parts will be needed for dv.
  • Another participant corrects the previous suggestion, asserting that dv should be tan x sec^3 x dx without the "x".
  • A later reply acknowledges the correction with appreciation.

Areas of Agreement / Disagreement

Participants generally agree on the approach of using integration by parts, but there is some uncertainty regarding the correct assignment of variables in the integration process.

Contextual Notes

There is a lack of consensus on the precise definitions of the variables u, du, v, and dv in the context of integration by parts, which may affect the clarity of the proposed solution.

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can anybody help me with this problem
Evaluate :
integral 3x (sinx/cos^4x) dx
 
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Is it \int \frac{3x\sin x}{\cos^{4} x}?

Rewrite it as 3\int x\tan x\ sec^{3} x and use integration by parts
 
Last edited:
i know the equation for intergration by parts is
intergral u dv = uv -intergral v du

can u tell me which variable is which?...u, du, v, dv=?...there seems to have 3 different variable.
 
Let u = x and dv = \ tan x \sec^{3} x. You will then need to use integration by parts on dv to get v.
 
Last edited:
I'm sure courtrigrad meant u= x and dv= tan x sec^3 xdx (with out the "x" in dv).
 
yep, thanks catching that :smile:
 

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