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indefinite integration of polynomial and trignometric functions

indefinite integral of $x^nsin(x)$Integrate $int_0^pixsin xover1+cos^2xdx$.Solve $int 3xcos(2x)dx$ with integration by partsintegration by parts of trig functionsIntegration techniques for $int x^3sin x^2,dx$Integrations by partsEvaluate $int e^2cos xcos 2x dx$How to solve this integration problem by parts and substitution?Indefinite Integration of a trig functionIntegral of $int_0^b cos(x)cos(frac a x)dx$

1

1

$begingroup$

integrate $$int frac(1+ x^2)(2+ x^2)(x cos x + sin x)^4dx$$
I have tried integration by parts but this x cos x + sin x part is creating problem so i tried substituting it, but unlike x sin x + cos x it is not reducing terms. I think something would be multiplied and divided in the first step, though I am not able to figure out what it is.

integration

share|cite|improve this question

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

asked Mar 20 at 18:48

user185442user185442

192

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Is this right so?
  $endgroup$
  – Dr. Sonnhard Graubner
  Mar 20 at 18:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes sir, it is and answer is ((x tan x -1)/(x + tan x)) +(1/3)*(((x tan x -1)^3)/(x + tan x)) + c but i do not know the solution
  $endgroup$
  – user185442
  Mar 21 at 17:42
  

  
  
  
  

add a comment | 

1

1

$begingroup$

integrate $$int frac(1+ x^2)(2+ x^2)(x cos x + sin x)^4dx$$
I have tried integration by parts but this x cos x + sin x part is creating problem so i tried substituting it, but unlike x sin x + cos x it is not reducing terms. I think something would be multiplied and divided in the first step, though I am not able to figure out what it is.

integration

share|cite|improve this question

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

asked Mar 20 at 18:48

user185442user185442

192

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Is this right so?
  $endgroup$
  – Dr. Sonnhard Graubner
  Mar 20 at 18:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  yes sir, it is and answer is ((x tan x -1)/(x + tan x)) +(1/3)*(((x tan x -1)^3)/(x + tan x)) + c but i do not know the solution
  $endgroup$
  – user185442
  Mar 21 at 17:42
  

  
  
  
  

add a comment | 

$begingroup$

integrate $$int frac(1+ x^2)(2+ x^2)(x cos x + sin x)^4dx$$
I have tried integration by parts but this x cos x + sin x part is creating problem so i tried substituting it, but unlike x sin x + cos x it is not reducing terms. I think something would be multiplied and divided in the first step, though I am not able to figure out what it is.

integration

share|cite|improve this question

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

asked Mar 20 at 18:48

user185442user185442

192

$endgroup$

share|cite|improve this question

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

asked Mar 20 at 18:48

user185442user185442

192

share|cite|improve this question

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

asked Mar 20 at 18:48

user185442user185442

192

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

edited Mar 20 at 18:55

Dr. Sonnhard Graubner

78.4k42867

asked Mar 20 at 18:48

user185442user185442

192

asked Mar 20 at 18:48

user185442user185442

192