/sci/ - Science & Math

[OP !!yzPI6QwWJCg No.4786608]

Hi,
I hope someone can help me with a (probably rather easy) integration problem. I just don't see the trick that's needed, I suppose, plus the task requires me to use partial integration as opposed to substitution or any other method, although other methods might be suited better.

<span class="math"> \int \sin^3(x) * \cos(x) dx[/spoiler]

My attempt was to set

a' = <span class="math"> \cos(x) [/spoiler]
a = <span class="math"> \sin(x) [/spoiler]
b = <span class="math"> \sin^3(x) [/spoiler]
b' = <span class="math"> 3\sin^2(x) * \cos(x) [/spoiler]

so

<span class="math"> \int \sin^3(x) * \cos(x) dx = \sin^4(x) - \int \sin(x) * (3(\sin^2(x)) * \cos(x)) dx [/spoiler]

Sadly, that doesn't help me much. Even if I partially integrate further, it just becomes a terrible mess. Any hints? I don't need a complete solution, just a hint would be helpful.

[Anonymous No.4786611]

Since the derivative of sinx is cosx according to chain rule you should get sin^3xcosx when differentiating (1/4)sin^4(x) + C, so thats the integral

[The Tourist !!zaCQyFZeSRS No.4786615]

I have no idea how to use the symbol notation on this board but you just need to go a few steps past the last line you have. Think of linearity.

[Anonymous No.4786618]

>>4786611
Please be trolling!

[OP !!yzPI6QwWJCg No.4786622]

>>4786615
The syntax is very similiar to the usual LaTeX syntax, and is used by typing math and /math in square brackets. It's a kind of programming language for mathematical texts etc.

[Anonymous No.4786624]

let me wolfram that for you...
http://www.wolframalpha.com/input/?i=integral%20of%20sin%5E3x*cosx&t=crmtb01

[Anonymous No.4786628]

The integral on the right is just 3 times the integral on the left. Add it to the other side and divide by 4, then you get sin^4(x)/4

[Anonymous No.4786630]

test
\lim_{x\to0}\int e^{x}dx

[Anonymous No.4786631]

<div class="math">\int f(x)^{n}f'(x)dx = \frac{f(x)^{n+1}}{n+1}</div>

[Anonymous No.4786634]

>>4786630
you need [math.] before and after each statment (take out the dot)

[OP !!yzPI6QwWJCg No.4786640]

>>4786628
That's the kind of hint I needed. Many thanks!

[Anonymous No.4787275]

>>4786608

I think your first integral there is just a simple substitution rule.

That is, it can be expressed in the form:

f(g(x)) * g'(x) * dx

This allows you to make a "u substitution" by setting u = g(x). You'll then substitute dx=du/u', cancel out your cosines, and then you'll get a much simpler integral to solve. Once you're done, get rid of the u by going back to its equivalent g(x).