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An A-level integral

I have decided to take a leaf out of @TeeEm's book :biggrin:

Evaluate

\displaystyle \int e^{x\sin x + \cos x} \left(\dfrac{x^4 \cos^3 x - x \sin x + \cos x}{x^2 \cos^2 x}\right) \ dx

I initially posted this on 'the hard integral thread', but I think it deserves a wider audience because, after all, it only requires knowledge of the regular A-level Maths syllabus :yep:

Enjoy!

(edited 8 years ago)

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Reply 1

TeeEm

Original post by Indeterminate

I have decided to take a leaf out of @TeeEm's book in order to invoke some kind of a discussion on this forum :biggrin:

Evaluate

\displaystyle \int e^{x\sin x + \cos x} \left(\dfrac{x^4 \cos^3 x - x \sin x + \cos x}{x^2 \cos^2 x}\right) \ dx

I initially posted this on 'the hard integral thread', but I think it deserves a wider audience because, after all, it only requires knowledge of the regular A-level Maths syllabus :yep:

Enjoy!

very good

Reply 2

Indeterminate

Original post by TeeEm

very good

Shame we haven't had any replies yet :frown:

Reply 3

TeeEm

Original post by Indeterminate

Shame we haven't had any replies yet :frown:

maths died about a year ago ...

Reply 4

Zacken

Original post by Indeterminate

Shame we haven't had any replies yet :frown:

I'd give it a bash but I'm swamped with FP3. :frown:

Reply 5

Indeterminate

Original post by Zacken

I'd give it a bash but I'm swamped with FP3. :frown:

Lol, that's fair enough :biggrin:

So I think it's time to tag a few people...

Reply 6

drandy76

I'll give it a try, be back soonish with my answer hopefully

Reply 7

KFazza

Spoiler

Posted from TSR Mobile

Reply 8

atsruser

Original post by Zacken

I'd give it a bash but I'm swamped with FP3. :frown:

I'd give it a bash but I can't be bothered as it looks hard.

Though maybe you can look for an IBP inspired approach? The exponential would seem to point that way.

Reply 9

Ayman!

Original post by Indeterminate

Lol, that's fair enough :biggrin:

So I think it's time to tag a few people...

I'm honoured to be tagged in one of Indeterminate's integral posts, but my integration skills are quite laughable. :colondollar:

I've attempted to separate them into individual functions using simplification and have tried trigonometric substitutions, but it's not looking too pretty... Any hints? :redface:

Reply 10

Indeterminate

Original post by aymanzayedmannan

I'm honoured to be tagged in one of Indeterminate's integral posts, but my integration skills are quite laughable. :colondollar:

I've attempted to separate them into individual functions using simplification and have tried trigonometric substitutions, but it's not looking too pretty... Any hints? :redface:

You don't need to use a substitution. Play around with what's inside the brackets and see what you get :biggrin:

Reply 11

drandy76

Spoiler

Posted from TSR Mobile

correct?

Original post by drandy76

Spoiler

Posted from TSR Mobile

Try differentiating that and then compare it to the expression to be integrated

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Reply 14

drandy76

Original post by KFazza

Try differentiating that and then compare it to the expression to be integrated

Posted from TSR Mobile

oh dear

Reply 15

Student403

I don't think this can be classed as a solution cause I did a lot of this question by observation which I tried to explain with the notes as I go along

IMPORTANT EDIT: at the end there should be a minus not a plus. IntA - IntB

But anyway is this correct? Hopefully you can follow along..

Spoiler

(edited 8 years ago)

Reply 16

Indeterminate