Mixing
How do I solve $int frac{xcos^2x + sin x}{cos^2x} e^{sin x} dx$?
3
$begingroup$
I tried the following:
Breaking up the fraction and applying parts to each of them.
Multiplying and dividing by $cos x$ and performing substitutions and parts
Breaking up into fractions, performing substitution and adding and subtracting by the differential of the former half, hoping that differentiating that would give the latter half.
I couldn't get an answer.
integration indefinite-integrals substitution
edited Jan 27 at 7:03
clathratus
5,1801438
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
$endgroup$
add a comment |
3
$begingroup$
I tried the following:
Breaking up the fraction and applying parts to each of them.
Multiplying and dividing by $cos x$ and performing substitutions and parts
Breaking up into fractions, performing substitution and adding and subtracting by the differential of the former half, hoping that differentiating that would give the latter half.
I couldn't get an answer.
integration indefinite-integrals substitution
edited Jan 27 at 7:03
clathratus
5,1801438
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
$endgroup$
1
$begingroup$
Are you absolutely sure this is the integral you wish to find? Carefully check what you have written for your integrand as a small typo could mean the world of difference between being able to find the integral in terms of elementary functions or not.
$endgroup$
– omegadot
Jan 27 at 7:36
$begingroup$
This is exactly the same integrand given in my workbook. So probably there is a printing mistake.
$endgroup$
– Sashank Sriram
Jan 27 at 8:04
$begingroup$
I believe as written your integral cannot be expressed in terms of elementary functions. If I make two very small changes in the integrand the resulting integral can be found in terms of elementary functions. The changed integral to find is: $$int frac{color{red} - x cos^{color{red} 3} x + sin x}{cos^2 x} e^{sin x} , dx$$
$endgroup$
– omegadot
Jan 27 at 8:13
$begingroup$
Thanks. I'll work on that, then.
$endgroup$
– Sashank Sriram
Jan 27 at 8:41
add a comment |
3
3
3
3
$begingroup$
I tried the following:
Breaking up the fraction and applying parts to each of them.
Multiplying and dividing by $cos x$ and performing substitutions and parts
Breaking up into fractions, performing substitution and adding and subtracting by the differential of the former half, hoping that differentiating that would give the latter half.
I couldn't get an answer.
integration indefinite-integrals substitution
edited Jan 27 at 7:03
clathratus
5,1801438
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
$endgroup$
I tried the following:
Breaking up the fraction and applying parts to each of them.
Multiplying and dividing by $cos x$ and performing substitutions and parts
Breaking up into fractions, performing substitution and adding and subtracting by the differential of the former half, hoping that differentiating that would give the latter half.
I couldn't get an answer.
integration indefinite-integrals substitution
integration indefinite-integrals substitution
edited Jan 27 at 7:03
clathratus
5,1801438
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
edited Jan 27 at 7:03
clathratus
5,1801438
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
edited Jan 27 at 7:03
clathratus
5,1801438
edited Jan 27 at 7:03
clathratus
5,1801438
edited Jan 27 at 7:03
clathratus
5,1801438
5,1801438
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
asked Jan 27 at 7:00
Sashank SriramSashank Sriram
444
444
1
$begingroup$
Are you absolutely sure this is the integral you wish to find? Carefully check what you have written for your integrand as a small typo could mean the world of difference between being able to find the integral in terms of elementary functions or not.
$endgroup$
– omegadot
Jan 27 at 7:36
$begingroup$
This is exactly the same integrand given in my workbook. So probably there is a printing mistake.
$endgroup$
– Sashank Sriram
Jan 27 at 8:04
$begingroup$
I believe as written your integral cannot be expressed in terms of elementary functions. If I make two very small changes in the integrand the resulting integral can be found in terms of elementary functions. The changed integral to find is: $$int frac{color{red} - x cos^{color{red} 3} x + sin x}{cos^2 x} e^{sin x} , dx$$
$endgroup$
– omegadot
Jan 27 at 8:13
$begingroup$
Thanks. I'll work on that, then.
$endgroup$
– Sashank Sriram
Jan 27 at 8:41
add a comment |
1
$begingroup$
Are you absolutely sure this is the integral you wish to find? Carefully check what you have written for your integrand as a small typo could mean the world of difference between being able to find the integral in terms of elementary functions or not.
$endgroup$
– omegadot
Jan 27 at 7:36
$begingroup$
This is exactly the same integrand given in my workbook. So probably there is a printing mistake.
$endgroup$
– Sashank Sriram
Jan 27 at 8:04
$begingroup$
I believe as written your integral cannot be expressed in terms of elementary functions. If I make two very small changes in the integrand the resulting integral can be found in terms of elementary functions. The changed integral to find is: $$int frac{color{red} - x cos^{color{red} 3} x + sin x}{cos^2 x} e^{sin x} , dx$$
$endgroup$
– omegadot
Jan 27 at 8:13
$begingroup$
Thanks. I'll work on that, then.
$endgroup$
– Sashank Sriram
Jan 27 at 8:41
1
1
$begingroup$
Are you absolutely sure this is the integral you wish to find? Carefully check what you have written for your integrand as a small typo could mean the world of difference between being able to find the integral in terms of elementary functions or not.
$endgroup$
– omegadot
Jan 27 at 7:36
$begingroup$
Are you absolutely sure this is the integral you wish to find? Carefully check what you have written for your integrand as a small typo could mean the world of difference between being able to find the integral in terms of elementary functions or not.
$endgroup$
– omegadot
Jan 27 at 7:36
$begingroup$
This is exactly the same integrand given in my workbook. So probably there is a printing mistake.
$endgroup$
– Sashank Sriram
Jan 27 at 8:04
$begingroup$
This is exactly the same integrand given in my workbook. So probably there is a printing mistake.
$endgroup$
– Sashank Sriram
Jan 27 at 8:04
$begingroup$
I believe as written your integral cannot be expressed in terms of elementary functions. If I make two very small changes in the integrand the resulting integral can be found in terms of elementary functions. The changed integral to find is: $$int frac{color{red} - x cos^{color{red} 3} x + sin x}{cos^2 x} e^{sin x} , dx$$
$endgroup$
– omegadot
Jan 27 at 8:13
$begingroup$
I believe as written your integral cannot be expressed in terms of elementary functions. If I make two very small changes in the integrand the resulting integral can be found in terms of elementary functions. The changed integral to find is: $$int frac{color{red} - x cos^{color{red} 3} x + sin x}{cos^2 x} e^{sin x} , dx$$
$endgroup$
– omegadot
Jan 27 at 8:13
$begingroup$
Thanks. I'll work on that, then.
$endgroup$
– Sashank Sriram
Jan 27 at 8:41
$begingroup$
Thanks. I'll work on that, then.
$endgroup$
– Sashank Sriram
Jan 27 at 8:41
add a comment |
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1
$begingroup$
Are you absolutely sure this is the integral you wish to find? Carefully check what you have written for your integrand as a small typo could mean the world of difference between being able to find the integral in terms of elementary functions or not.
$endgroup$
– omegadot
Jan 27 at 7:36
$begingroup$
This is exactly the same integrand given in my workbook. So probably there is a printing mistake.
$endgroup$
– Sashank Sriram
Jan 27 at 8:04
$begingroup$
I believe as written your integral cannot be expressed in terms of elementary functions. If I make two very small changes in the integrand the resulting integral can be found in terms of elementary functions. The changed integral to find is: $$int frac{color{red} - x cos^{color{red} 3} x + sin x}{cos^2 x} e^{sin x} , dx$$
$endgroup$
– omegadot
Jan 27 at 8:13
$begingroup$
Thanks. I'll work on that, then.
$endgroup$
– Sashank Sriram
Jan 27 at 8:41