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Integration using parts

0

$begingroup$

I am struggling to evaluate this integral:
$$
int e^{(mu +r)t+frac{r}{alpha}sin(alpha t)}cos(alpha t)dt
$$
The integration just gets harder and harder when integrating by parts! Any tips?

Thanks in advance!

calculus integration

share|cite|improve this question

edited Mar 25 at 17:31

Théophile

20.5k13047

asked Mar 25 at 17:26

benharmerbenharmer

114

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Which equation?
  $endgroup$
  – José Carlos Santos
  Mar 25 at 17:27
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Make sure you're choosing the right parts. What's your $u$ and $dv$?
  $endgroup$
  – Michael Biro
  Mar 25 at 17:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Wolfram Alpha cannot solve analytically even the greatly simplified case of $mu=0,r=alpha=1$. Is this an expression you arrived at on your own?
  $endgroup$
  – jawheele
  Mar 25 at 19:04
  

  
  
  
  

add a comment | 

0

$begingroup$

I am struggling to evaluate this integral:
$$
int e^{(mu +r)t+frac{r}{alpha}sin(alpha t)}cos(alpha t)dt
$$
The integration just gets harder and harder when integrating by parts! Any tips?

Thanks in advance!

calculus integration

share|cite|improve this question

edited Mar 25 at 17:31

Théophile

20.5k13047

asked Mar 25 at 17:26

benharmerbenharmer

114

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Which equation?
  $endgroup$
  – José Carlos Santos
  Mar 25 at 17:27
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Make sure you're choosing the right parts. What's your $u$ and $dv$?
  $endgroup$
  – Michael Biro
  Mar 25 at 17:31
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Wolfram Alpha cannot solve analytically even the greatly simplified case of $mu=0,r=alpha=1$. Is this an expression you arrived at on your own?
  $endgroup$
  – jawheele
  Mar 25 at 19:04
  

  
  
  
  

add a comment | 

$begingroup$

I am struggling to evaluate this integral:
$$
int e^{(mu +r)t+frac{r}{alpha}sin(alpha t)}cos(alpha t)dt
$$
The integration just gets harder and harder when integrating by parts! Any tips?

Thanks in advance!

calculus integration

share|cite|improve this question

edited Mar 25 at 17:31

Théophile

20.5k13047

asked Mar 25 at 17:26

benharmerbenharmer

114

$endgroup$

share|cite|improve this question

edited Mar 25 at 17:31

Théophile

20.5k13047

asked Mar 25 at 17:26

benharmerbenharmer

114

share|cite|improve this question

edited Mar 25 at 17:31

Théophile

20.5k13047

asked Mar 25 at 17:26

benharmerbenharmer

114

edited Mar 25 at 17:31

Théophile

20.5k13047

edited Mar 25 at 17:31

Théophile

20.5k13047

asked Mar 25 at 17:26

benharmerbenharmer

114

asked Mar 25 at 17:26

benharmerbenharmer

114

1 Answer
1

active

oldest

votes

0

$begingroup$

Hint: write $$e^{(mu+r)t+frac ralphasin(alpha t)}cos(alpha t)=e^{(mu+r)t}e^{frac ralphasin(alpha t)}cos(alpha t)$$Notice that the last two terms have trigonometric functions with the argument $(alpha t)$. This indicates there may be a connection between these two terms. What happens if you integrate $e^{frac ralphasin(alpha t)}cos(alpha t)$?

share|cite|improve this answer

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339

$endgroup$

add a comment | 

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0

$begingroup$

Hint: write $$e^{(mu+r)t+frac ralphasin(alpha t)}cos(alpha t)=e^{(mu+r)t}e^{frac ralphasin(alpha t)}cos(alpha t)$$Notice that the last two terms have trigonometric functions with the argument $(alpha t)$. This indicates there may be a connection between these two terms. What happens if you integrate $e^{frac ralphasin(alpha t)}cos(alpha t)$?

share|cite|improve this answer

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339

$endgroup$

add a comment | 

0

$begingroup$

Hint: write $$e^{(mu+r)t+frac ralphasin(alpha t)}cos(alpha t)=e^{(mu+r)t}e^{frac ralphasin(alpha t)}cos(alpha t)$$Notice that the last two terms have trigonometric functions with the argument $(alpha t)$. This indicates there may be a connection between these two terms. What happens if you integrate $e^{frac ralphasin(alpha t)}cos(alpha t)$?

share|cite|improve this answer

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339

$endgroup$

add a comment | 

$begingroup$

Hint: write $$e^{(mu+r)t+frac ralphasin(alpha t)}cos(alpha t)=e^{(mu+r)t}e^{frac ralphasin(alpha t)}cos(alpha t)$$Notice that the last two terms have trigonometric functions with the argument $(alpha t)$. This indicates there may be a connection between these two terms. What happens if you integrate $e^{frac ralphasin(alpha t)}cos(alpha t)$?

share|cite|improve this answer

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339

$endgroup$

share|cite|improve this answer

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339

answered Mar 25 at 17:41

John DoeJohn Doe

12.1k11339