Integral of a function of phi and sin(phi) in denominator
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I need to solve an integral for my master thesis in physics, but I do not know how to even start. The integral is
$int_{-pi/2}^{pi/2} frac{1}{b+sin^2(phi)} cdot frac{1}{a^2+phi^2} dphi$
Both a and b are positive and bigger than 0, so the integral should converge.
I tried to think of a Weierstrass Substitution, but could not find a suitable one.
Also, I could not apply the Residue theorem, since I do not know which contours to use.
I need the result dependent on a and b.
Can you give me any tipps?
integration
asked Nov 13 at 16:17
Daniel R
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Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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up vote
1
down vote
favorite
I need to solve an integral for my master thesis in physics, but I do not know how to even start. The integral is
$int_{-pi/2}^{pi/2} frac{1}{b+sin^2(phi)} cdot frac{1}{a^2+phi^2} dphi$
Both a and b are positive and bigger than 0, so the integral should converge.
I tried to think of a Weierstrass Substitution, but could not find a suitable one.
Also, I could not apply the Residue theorem, since I do not know which contours to use.
I need the result dependent on a and b.
Can you give me any tipps?
integration
asked Nov 13 at 16:17
Daniel R
61
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Looks nasty! I don't see any way other than doing it numerically unfortunately.
– Richard Martin
Nov 13 at 16:37
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I need to solve an integral for my master thesis in physics, but I do not know how to even start. The integral is
$int_{-pi/2}^{pi/2} frac{1}{b+sin^2(phi)} cdot frac{1}{a^2+phi^2} dphi$
Both a and b are positive and bigger than 0, so the integral should converge.
I tried to think of a Weierstrass Substitution, but could not find a suitable one.
Also, I could not apply the Residue theorem, since I do not know which contours to use.
I need the result dependent on a and b.
Can you give me any tipps?
integration
asked Nov 13 at 16:17
Daniel R
61
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I need to solve an integral for my master thesis in physics, but I do not know how to even start. The integral is
$int_{-pi/2}^{pi/2} frac{1}{b+sin^2(phi)} cdot frac{1}{a^2+phi^2} dphi$
Both a and b are positive and bigger than 0, so the integral should converge.
I tried to think of a Weierstrass Substitution, but could not find a suitable one.
Also, I could not apply the Residue theorem, since I do not know which contours to use.
I need the result dependent on a and b.
Can you give me any tipps?
integration
integration
asked Nov 13 at 16:17
Daniel R
61
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 16:17
Daniel R
61
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 16:17
Daniel R
61
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Nov 13 at 16:17
Daniel R
61
asked Nov 13 at 16:17
Daniel R
61
61
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Daniel R is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
2
Looks nasty! I don't see any way other than doing it numerically unfortunately.
– Richard Martin
Nov 13 at 16:37
add a comment |
2
Looks nasty! I don't see any way other than doing it numerically unfortunately.
– Richard Martin
Nov 13 at 16:37
2
2
Looks nasty! I don't see any way other than doing it numerically unfortunately.
– Richard Martin
Nov 13 at 16:37
Looks nasty! I don't see any way other than doing it numerically unfortunately.
– Richard Martin
Nov 13 at 16:37
add a comment |
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Daniel R is a new contributor. Be nice, and check out our Code of Conduct.
Daniel R is a new contributor. Be nice, and check out our Code of Conduct.
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Looks nasty! I don't see any way other than doing it numerically unfortunately.
– Richard Martin
Nov 13 at 16:37