How to Integrate cosx/((sinx)^2 + 1) with Respect to x

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Discussion Overview

The discussion revolves around the integration of trigonometric functions, specifically focusing on the integral of cos(x)/((sin(x))^2 + 1) with respect to x. Participants explore substitution methods and tackle related integrals, including more complex forms involving sin(x) and exponential functions.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant asks how to integrate cos(x)/((sin(x))^2 + 1) with respect to x.
  • Another participant suggests using the substitution u = sin(x) for the first integral.
  • A third participant expresses appreciation for the suggestion of substitution.
  • A new integral is introduced involving cos(x)/(sin(x))^9, which one participant finds challenging.
  • Participants again suggest using u = sin(x) for the new integral.
  • Another participant shifts the topic to the integral of 10^x, asking for guidance.
  • Responses include rewriting 10^x as e^(x ln(10)) and suggesting u = 10^x as a substitution.

Areas of Agreement / Disagreement

Participants generally agree on the use of substitution methods for integration, but the discussion includes multiple integrals and varying levels of complexity, with no consensus on the difficulty of the problems presented.

Contextual Notes

Some participants do not provide detailed steps for the integrals, and there may be assumptions about the familiarity with substitution techniques that are not explicitly stated.

tmozam
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how do i integrate -- cosx/((sinx)^2 + 1) with respect to x
thanks for your help
 
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Set u=sin(x)
 
oh wow , why didnt i think of that ?
thanks a lot
 
what is the integral of ∫ cosx/(sinx)^9 with respect to x.
i think this one is a bit challenging
 
Just let u = sin(x) again...
 
how about integral of 10^x with respect to x
 
write [itex]10^x = e^{xln10}[/itex]
 
Or, set u=10^x
 

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