Mixing
How to evaluate $int frac{dx}{(2x+1)sqrt{3x+2}}$
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 '18 at 11:03
José Carlos Santos
151k22123224
asked Nov 21 '18 at 10:34
emil
417410
add a comment |
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 '18 at 11:03
José Carlos Santos
151k22123224
asked Nov 21 '18 at 10:34
emil
417410
add a comment |
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 '18 at 11:03
José Carlos Santos
151k22123224
asked Nov 21 '18 at 10:34
emil
417410
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 '18 at 11:03
José Carlos Santos
151k22123224
asked Nov 21 '18 at 10:34
emil
417410
edited Nov 21 '18 at 11:03
José Carlos Santos
151k22123224
asked Nov 21 '18 at 10:34
emil
417410
edited Nov 21 '18 at 11:03
José Carlos Santos
151k22123224
edited Nov 21 '18 at 11:03
José Carlos Santos
151k22123224
edited Nov 21 '18 at 11:03
José Carlos Santos
151k22123224
151k22123224
asked Nov 21 '18 at 10:34
emil
417410
asked Nov 21 '18 at 10:34
emil
417410
asked Nov 21 '18 at 10:34
emil
417410
417410
add a comment |
add a comment |
3 Answers
3
active
oldest
votes
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 '18 at 10:39
José Carlos Santos
151k22123224
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 '18 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 '18 at 11:07
add a comment |
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
add a comment |
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 '18 at 10:38
Martund
1,405212
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
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 '18 at 10:39
José Carlos Santos
151k22123224
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 '18 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 '18 at 11:07
add a comment |
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 '18 at 10:39
José Carlos Santos
151k22123224
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 '18 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 '18 at 11:07
add a comment |
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 '18 at 10:39
José Carlos Santos
151k22123224
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 '18 at 10:39
José Carlos Santos
151k22123224
edited Nov 21 '18 at 10:46
answered Nov 21 '18 at 10:39
José Carlos Santos
151k22123224
answered Nov 21 '18 at 10:39
José Carlos Santos
151k22123224
answered Nov 21 '18 at 10:39
José Carlos Santos
151k22123224
151k22123224
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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 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 '18 at 11:07
add a comment |
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
add a comment |
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
add a comment |
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
Hint:
Set $sqrt{3x+2}=yimpliesdfrac{3dx}{2sqrt{3x+2}}=dy$
$3x+2=y^2iff2x+1=?$
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
answered Nov 21 '18 at 10:42
lab bhattacharjee
223k15156274
223k15156274
add a comment |
add a comment |
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 '18 at 10:38
Martund
1,405212
add a comment |
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 '18 at 10:38
Martund
1,405212
add a comment |
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 '18 at 10:38
Martund
1,405212
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 '18 at 10:38
Martund
1,405212
answered Nov 21 '18 at 10:38
Martund
1,405212
answered Nov 21 '18 at 10:38
Martund
1,405212
answered Nov 21 '18 at 10:38
Martund
1,405212
1,405212
add a comment |
add a comment |
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