Integration do i use substitution or parts?

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Discussion Overview

The discussion centers around the integration of the function sin(√(1 + x)). Participants explore different methods for solving the integral, including substitution and integration by parts.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using substitution with u = √(1 + x) as a starting point.
  • Another participant proposes expressing u as (1 + x)^(1/2) and indicates that integration by parts could be applied after substitution.
  • James expresses confusion about the next steps after arriving at the integral of u * sin(u) du.
  • A later reply reiterates the use of integration by parts, providing a breakdown of the process involving u and its derivative.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the best approach, as different methods are suggested and explored without a definitive resolution.

Contextual Notes

There are unresolved steps in the integration process, and the discussion reflects varying levels of understanding and clarity regarding the application of integration techniques.

james5
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Hi,

i am stumped on how to start this:

integration of sin(ROOT(1 + x))

so, basically sin of square root 1 + x

thanks

James
 
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I think you'll end up using both, try the substitution u=sqrt(1+x)
 
hi

we can

u=(1+x)^(1\2)
du.u=dx
integrat(u.sin(u).du)

and you can use parts to compleat
 
thanks!

i get now to

INTEGRAL(u * sin(u)) du

ok, so now what should I do?

thanks

James
 
nvm, i got it
 
hi

u.sin(u)du

and you can use parts to compleat

z=u ...dm=sin(u)du
dz=du...m=-cos(u)

= -u.cos(u)-INTEGRAL(-cos(u)du)

after

u=(1+x)^(1\2)

and substitut by (1+x)^(1\2)

tanks's
 

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