# Integrate cos(sin(x))

1. ## cos(sinx)

can anyone give a result for this integration

∫cos(sin(θ)) dθ

unlimited or limited by any values may reduce any complexity
Roshdy

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2. ## integrate cos(cos x)

I highly doubt that there is a finite expression of that integral. It can be expressed by a series if certain integration limits are applied.

1 members found this post helpful.

3. ## integration sin(sin(x))

Hi,
If this integral has limits of 0 to pi it will be equal to pi*J(0,x) where J(0,x) is Bessel function of order zero.
Regards,

1 members found this post helpful.

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4. ## integrate cos(cos(x))

cos(sinx)= cos(cos(90-x))=cos^2(90-x)

i.e ∫cos²(90-x)dx which can be ∫ed easily right.

5. ## integral sin catalan

Hi,
This is not correct because cos(cos(90-x) is not equal to cos^(90-x) whis is equal to cos(90-x)*cos(90-x).
It can only be integrated numerically unless it has limits of 0 to pi where it's Bessel function..
Regards,

6. ## cos integrates to sin

right
cos(cos(x)) doesn't equal to cos^2(x)
Roshdy

7. ## Re: Integrate cos(sin(x))

What will be the integral
$3\frac{1}{\pi}\int_0^\picos(cos(\theta))d\theta$

M

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8. ## Re: Integrate cos(sin(x))

Originally Posted by magnetra
What will be the integral
$3\frac{1}{\pi}\int_0^\picos(cos(\theta))d\theta$
See previous messages.

$3\int_{0}^{\pi}\cos(\sin\tau)\,\mathrm{d}\tau=\int_{0}^{\pi}\cos(\cos\tau)\,\mathrm{d}\tau$

--> $3\frac{1}{\pi}\int_{0}^{\pi}\cos(\cos\tau)\,\mathrm{d}\tau=J_0(1)=0.7651976865$

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