How to evaluate $int frac{dx}{(2x+1)sqrt{3x+2}}$
up vote
1
down vote
favorite
Evaluate $$int frac{dx}{(2x+1)sqrt{3x+2}}$$
I used the substitution,$$t=3x+2$$
Which leads to $$dt=3dx$$
But then the denominator becomes much more complex to simplify(I can show my working if necessary). Is my substitution wrong?
Please Help!
integration indefinite-integrals
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
asked Nov 21 at 10:34
emil
415410
add a comment |
up vote
1
down vote
favorite
Evaluate $$int frac{dx}{(2x+1)sqrt{3x+2}}$$
I used the substitution,$$t=3x+2$$
Which leads to $$dt=3dx$$
But then the denominator becomes much more complex to simplify(I can show my working if necessary). Is my substitution wrong?
Please Help!
integration indefinite-integrals
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
asked Nov 21 at 10:34
emil
415410
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Evaluate $$int frac{dx}{(2x+1)sqrt{3x+2}}$$
I used the substitution,$$t=3x+2$$
Which leads to $$dt=3dx$$
But then the denominator becomes much more complex to simplify(I can show my working if necessary). Is my substitution wrong?
Please Help!
integration indefinite-integrals
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
asked Nov 21 at 10:34
emil
415410
Evaluate $$int frac{dx}{(2x+1)sqrt{3x+2}}$$
I used the substitution,$$t=3x+2$$
Which leads to $$dt=3dx$$
But then the denominator becomes much more complex to simplify(I can show my working if necessary). Is my substitution wrong?
Please Help!
integration indefinite-integrals
integration indefinite-integrals
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
asked Nov 21 at 10:34
emil
415410
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
asked Nov 21 at 10:34
emil
415410
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
edited Nov 21 at 11:03
José Carlos Santos
147k22117218
147k22117218
asked Nov 21 at 10:34
emil
415410
asked Nov 21 at 10:34
emil
415410
asked Nov 21 at 10:34
emil
415410
415410
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
up vote
3
down vote
accepted
If you do $x=dfrac{y^2-2}3$ and $mathrm dx=dfrac23y,mathrm dy$, then your function becomes a rational function (because then $3x+2=y^2$).
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
1
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
add a comment |
up vote
3
down vote
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
add a comment |
up vote
1
down vote
You should substitute $3x+2 = t^2$, then the given integral can be solved in the next step using the direct formula.
answered Nov 21 at 10:38
Martund
1,262212
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
If you do $x=dfrac{y^2-2}3$ and $mathrm dx=dfrac23y,mathrm dy$, then your function becomes a rational function (because then $3x+2=y^2$).
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
1
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
add a comment |
up vote
3
down vote
accepted
If you do $x=dfrac{y^2-2}3$ and $mathrm dx=dfrac23y,mathrm dy$, then your function becomes a rational function (because then $3x+2=y^2$).
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
1
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
If you do $x=dfrac{y^2-2}3$ and $mathrm dx=dfrac23y,mathrm dy$, then your function becomes a rational function (because then $3x+2=y^2$).
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
If you do $x=dfrac{y^2-2}3$ and $mathrm dx=dfrac23y,mathrm dy$, then your function becomes a rational function (because then $3x+2=y^2$).
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
edited Nov 21 at 10:46
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
answered Nov 21 at 10:39
José Carlos Santos
147k22117218
147k22117218
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
1
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
add a comment |
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
1
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
Nice Substitution! Then it can be simplified to partial fractions to get an answer. Would you mind telling me how to find reference for these kind of substitutions? Because I find it hard to get the proper substitution for most problems. Thanks.
– emil
Nov 21 at 11:04
1
1
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
@emil I am not aware of a good reference for this. Perhaps that you might consider asking that as another question. In this case, I just thought that doing $3x+2=y^2$ would eliminate the square root.
– José Carlos Santos
Nov 21 at 11:07
add a comment |
up vote
3
down vote
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
add a comment |
up vote
3
down vote
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
add a comment |
up vote
3
down vote
up vote
3
down vote
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
answered Nov 21 at 10:42
lab bhattacharjee
222k15155273
222k15155273
add a comment |
add a comment |
up vote
1
down vote
You should substitute $3x+2 = t^2$, then the given integral can be solved in the next step using the direct formula.
answered Nov 21 at 10:38
Martund
1,262212
add a comment |
up vote
1
down vote
You should substitute $3x+2 = t^2$, then the given integral can be solved in the next step using the direct formula.
answered Nov 21 at 10:38
Martund
1,262212
add a comment |
up vote
1
down vote
up vote
1
down vote
You should substitute $3x+2 = t^2$, then the given integral can be solved in the next step using the direct formula.
answered Nov 21 at 10:38
Martund
1,262212
You should substitute $3x+2 = t^2$, then the given integral can be solved in the next step using the direct formula.
answered Nov 21 at 10:38
Martund
1,262212
answered Nov 21 at 10:38
Martund
1,262212
answered Nov 21 at 10:38
Martund
1,262212
answered Nov 21 at 10:38
Martund
1,262212
1,262212
add a comment |
add a comment |
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