Now all these integrals I post aren't in vain! The reason I do this is because I am conducting a study/project for school that in the long term will hopefully produce a booklet containing the most down to earth intuitive integration techniques known to highschooldom!

So I am going to do a couple of integrals..and if you see a more intutive way of doing them I would really appreciate it if you would post your way! Thanks so much...all in this work in the name of math

We will start easy...how intuitive do you think the method I always preach on posts of getting integrals into by constant manipulation is?

For example if I wrote something to the effect of

and now I will just do a couple without a small oration before hand

Let

Then

So we have

Using PFD we see that

Integrating we get

Back subbing we get

The next one is

Let

THen

So we have

by PFD we have

Integrating we get

Making our back sub we get

The last one is

Letting

THen

Subbing we have

Which then yields

Back subbing we get

So if anyone sees an easier way to do these please do tell! I need as much imput as possible for this booklet