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Integration help pleasee

How do I integrate 1/(3x^2 +4) ?

The answer I got was 1/(3x) ln|3x^2+4| but not sure if this is right

Thank you so much x
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Notnek
21
Original post by shle3brown
How do I integrate 1/(3x^2 +4) ?

The answer I got was 1/(3x) ln|3x^2+4| but not sure if this is right

Thank you so much x

No that's not right. I may be wrong but it looks like you've tried to use some kind of recognition/reverse chain rule incorrectly here. You can use recognition to integrate to ln if the numerator is a constant away from the derivative of the denominator. But this is not the case here. Try differentiating your result to see that it isn't right.

For this integral you need to use a tan substitution or use your formula book after putting the denominator in another form. Can I just check : is this a question from further maths?
(edited 6 years ago)
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Avatar for shle3brown
shle3brown
OP
8
Original post by Notnek
No that's not right. I may be wrong but it looks like you've tried to use some kind of recognition/reverse chain rule incorrectly here. You can use recognition to integrate to ln if the numerator is a constant away from the derivative of the denominator. But this is not the case here. Try differentiating your result to see that it isn't right.

For this integral you need to use a tan substitution or use your formula book after putting the denominator in another form. Can I just check : is this a question from further maths?


Thanks for the help. It's from a D1 question from a pre u revision pack so probably
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Notnek
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Original post by shle3brown
Thanks for the help. It's from a D1 question from a pre u revision pack so probably

I'm not familiar with pre-U. Do you know about trig substitutions and how to deal with integrals of the form

∫1a2+x2 dx\displaystyle \int \frac{1}{a^2+x^2} \ dx

Does this ring any bells?
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Avatar for shle3brown
shle3brown
OP
8
Original post by Notnek
I'm not familiar with pre-U. Do you know about trig substitutions and how to deal with integrals of the form

∫1a2+x2 dx\displaystyle \int \frac{1}{a^2+x^2} \ dx

Does this ring any bells?


It's in between further maths and regular A level.

I haven't come across anything like this but I'll see how I get on form here - cheers :smile:
Original post by shle3brown
How do I integrate 1/(3x^2 +4) ?

The answer I got was 1/(3x) ln|3x^2+4| but not sure if this is right

Thank you so much x


No as the numerator isn’t the differential of the denominator. I haven’t seen a question like this before so my help is limited to that, sorry.

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