Integration mega collection

I am attaching in this thread an integration booklet with 622 indefinite integrals at present ( 2 new ones to be added shortly)

This is the student version of the booklet which has no answers or solutions.
(A carbon copy of this document with answers and full solutions also exists but it is too large to attach here)

Can you suggest any decent "beautifully disgusting" integrals to add to this collection.
Indefinite integrals only please.
(undergrad techniques are ok, within reasonable difficulty)


integration_indefinite_mixed_up_student_version_condense.pdf


The booklet is not in strict "hardness" order but overall the questions get progressively harder

Many thanks

Note that at Q350 onwards a large proportion of integrals will be only accessible to further mathematicians

The booklet is not in strict "hardness" order but overall the questions get progressively harder

This should be the new FP3 exam : attempt as many of the 622 integrals as you can before the time runs out / your brain explodes.

But seriously, this is an extremely useful set of questions - one of the best further maths resources I've see in a while.

My suggestion for a disgusting integral:

$\displaystyle \int \frac{1}{(\cos^2 x +4\sin x - 5)\cos x} \ dx$

Probably more because of it's length as opposed to its difficulty.

this one looks simple (i dare ya!):

$\displaystyle \int \frac{\sin(x)}{1-\tan(x)}dx$

(equivalent to $\displaystyle \int \frac{\sin(x)\cos(x)}{\cos(x)-\sin(x)}dx$ )

definitely to be tried ... If it is in the list it will be added.

Sorry I cannot rep you cause I did rep today your contribution into a limits question.

Thanks

it`s an absolute bitch to do! - wouldn`t think it by looking, though!

The booklet is not in strict "hardness" order but overall the questions get progressively harder

$\int cos^n(x)dx, n \in \mathbb{N}$
$\int sin^n(x)dx, n \in \mathbb{N}$
$\int tan^n(x)dx, n \in \mathbb{N}$

Also, wolfram alpha will give you answers in terms of hyper-geometric functions but you do not need them if you consider the different cases resulting from different choices of n.

up to n=4 i have these I think

after 5 you really need reduction formulas for indefinite integrals, I know no other technique

hint: binomial expansion but need to write cos, sin, or tan in a different form...

hint: binomial expansion but need to write cos, sin, or tan in a different form...

you mean the $\displaystyle cos(x)=\frac{1}{2}(z+\frac{1}{z})$ etc thingy...?

(i don`t know how to make brackets bigger in LaTex)

... very clever ...

Try this one:

$\int e^{\alpha x}[\ cos(\beta x)+ \sin(\gamma x)] dx$

$\int cos^n(x)dx, n \in \mathbb{N}$
$\int sin^n(x)dx, n \in \mathbb{N}$
$\int tan^n(x)dx, n \in \mathbb{N}$

Also, wolfram alpha will give you answers in terms of hyper-geometric functions but you do not need them if you consider the different cases resulting from different choices of n.




Good old 622: $\int \sqrt{tan(x)} dx$ that was on one of my first (undergrad) uni problem sheets