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p3 integration

Integrate sin x cos^4 x

Please can someone tell me what method to use and how it can be integrated.
Reply 1
Avatar for RichE
RichE
15
Substitution with u = cosx
Reply 2
Avatar for Jackal123
Jackal123
OP
how do you know that?
And where would I go from there?

Cheers
Reply 3
Avatar for Font
Font
Jackal123
Integrate sin x cos^4 x

Please can someone tell me what method to use and how it can be integrated.

integrate it using "recognition"....answer by looking at it is -(1/5) * cos^5 x, or you can use a substituion of u = sin x.

The easiest method is to look at it. you know the rule for differentiating something like sin ^ n x and cos ^ n x...from standard results. Apply the reverse principle to your question, and bingo, you have it:biggrin:...hope it helps

Phil
Reply 4
Avatar for Newton
Newton
f(x)=(sinx)((cosx)^4)

INTf(x)dx

Let u=cosx

f(x) then becomes f(u) as:

f(x)=(-(du/dx))(u^4)dx

dx cancel:

Therefore:

-INT(u^4)du

=>=-(1/5)(u^5)+C

*u=cosx

=>=-(1/5)((cosx)^5)

Newton.
Jackal123
Integrate sin x cos^4 x dx

Int. sinx.cos^4x dx. = - Int. (-sinx).(cosx)^4 dx. = -(cos^5x)/5 + k

Use: Int. f ' (x). [f(x)]^n dx = {[f(x)]^(n + 1)}/(n + 1) + k

Nima
Reply 6
Avatar for Jackal123
Jackal123
OP
What method would I use to integrate cosec 2x cot 2x ?

Please just tell me what method to use and then i will try the rest.

cheers
Reply 7
Avatar for RichE
RichE
15
Jackal123
What method would I use to integrate cosec 2x cot 2x ?

Please just tell me what method to use and then i will try the rest.

cheers


Rewrite it in terms of sin2x's and cos2x's and use a substitution similar to the previous example.

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