Trig Integration: Integrating (sinx)^3 * cosx with Respect to x

[QueenFisher]

integrate with respect to x: (sinx)^3 * cosx

i have no idea where to start, can anyone help me? I've looked at differentials of other trig functions but i can't see any that would help

 

[benorin]

Use a "u substitution".

 

[QueenFisher]

what do you mean?

 

[Lyuokdea]

you want to use a u substitution. Find a value in your expression to be u, and find another one to be du.

~Lyuokdea

 

[benorin]

what do you mean?

How would you integrate $$\int (x^2+7)^3 \cdot 2x \,dx$$ ?

 

[tophman]

Use U sub. as indicated before. Let your U = sin(x) . Work it from there

 

[VietDao29]

integrate with respect to x: (sinx)^3 * cosx

i have no idea where to start, can anyone help me? I've looked at differentials of other trig functions but i can't see any that would help

If your sine function is raised to an odd power, it's commonly to let u = cos x, and work from there.
If your cosine function is raised to an odd power, it's commonly to let u = sin x, and work from there.
If both are raised to an odd power, then you can either let u = sin x, or u = cos x.
Note that, you should sometimes need to use the Pythagorean identity: sin²x + cos²x = 1, to solve your problem.
I'll give you an example:
-----------
Example:
$$\int \cos x \sin ^ 2 x dx$$
cos x is raised to the power 1, hence it's an odd power, let u = sin x.
u = sin x => du = cos x dx, right? Substitute that into your integral, we have:
$$\int u ^ 2 du = \frac{u ^ 3}{3} + C$$
Change u back to x, gives:
$$\int \cos x \sin ^ 2 x dx = \frac{\sin ^ 3 x}{3} + C$$
Can you go from here? :)

 

[QueenFisher]

i've never done anything like that before and i don't quite understand it

 

[misskitty]

Let me see if I can help you.

~Kitty

 

[misskitty]

Let me see if I have this correct, you have:

sine of x cubed times cosine of x right?

~Kitty

 

[misskitty]

Please don't take this as attacking. Have you been exposed to u substitution? I'm assuming you have.

~Kitty

 

[misskitty]

My process was about the same as VietDao. I'm sorry.

~Kitty

 

[Pseudo Statistic]

Too many posts... :\
Dude, if you didn't take this in class, read off this site for help. :}

 

[QueenFisher]

Please don't take this as attacking. Have you been exposed to u substitution? I'm assuming you have.

~Kitty

unfortunately not. but it turns out i didn't have to do it after all - it was off-the-syllabus stuff

 

[vaishakh]

As Viet told take u = cosx.
Then find du/dxand the relation between both to replace du in place of dx in the integration

 

[arildno]

Hmm..use of u=sinx is simpler in this case.

 

[QueenFisher]

the only u substitution I've used is in differentiation using the chain rule