Integrate (x^2)dx: Solution & Hint

[dnt]

Homework Statement

how do you integrate (xcox)dx

Homework Equations

n/a

The Attempt at a Solution

ive gone through so many ways that I've learned how to integrate problems and i cannot figure this one out. can someone just give me a hint on how to start it? thanks. (i have a feeling this is easy and I am overlooking a really basic way of doing it)

 

[VietDao29]

When seeing a product of a polynomial and e^x, or some kind of trigonometry functions. One should think about Integrate by Parts.
By letting u = the polynomial, in this case u = x.
And dv = the rest.
By the way, is your problem:
$$\int x \cos x dx \quad \mbox{or} \quad \int x \cot x dx$$?
Can you go from here? :)

 

[neutrino]

Integration by parts.

 

[neutrino]

By letting u = the polynomial, in this case u = x.
And dv = the rest.

I do not know if this mnemonic is taught everywhere, but when I was in school learning integration by parts, we were asked to remember ILATE, without justification, when deciding which part is to be u and which is to be dv. Of course, this rule need not work every time.

Inverse(Trigonometric)-Logarithmic-Algebraic-Trigonometric-Exponential.

The one that comes before the other will be u.

 

[dnt]

thanks. i knew it was easier than i thought.

and btw it was cos (forgot the s)

 

[VietDao29]

I do not know if this mnemonic is taught everywhere, but when I was in school learning integration by parts, we were asked to remember ILATE, without justification, when deciding which part is to be u and which is to be dv. Of course, this rule need not work every time.

Inverse(Trigonometric)-Logarithmic-Algebraic-Trigonometric-Exponential.

The one that comes before the other will be u.

Well, yes, some of the textbooks here do mention it. However, the are very rare, I think.
Btw, I don't know what it's called in English. Since, I am not a native-English speaker. Still have to learn a lot.
So yeah, thanks for the info. :)