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# Integrate cos(sin(x))

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#### Roshdy

##### Member level 3
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

#### steve10

##### Full Member level 3
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.

### Roshdy

Points: 2

#### tantoun2004

##### Member level 1
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,

### Roshdy

Points: 2

#### venkateshr

##### Member level 3
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.

#### tantoun2004

##### Member level 1
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,

#### Roshdy

##### Member level 3
cos integrates to sin

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

#### magnetra

##### Full Member level 5
What will be the integral
$\frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta$

M

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#### _Eduardo_

##### Full Member level 5
magnetra said:
What will be the integral
$\frac{1}{\pi} \int_0^\pi cos(cos(\theta)) d\theta$

See previous messages.

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

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

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