Calculus Examples

$\int \cos (x) \cos (\sin (x)) d x$

Let $u = \sin (x)$ . Then $d u = \cos (x) d x$ , so $\frac{1}{\cos (x)} d u = d x$ . Rewrite using $u$ and $d$ $u$ .

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Let $u = \sin (x)$ . Find $\frac{d u}{d x}$ .

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Differentiate $\sin (x)$ .

$\frac{d}{d x} [\sin (x)]$

The derivative of $\sin (x)$ with respect to $x$ is $\cos (x)$ .

$\cos (x)$

Rewrite the problem using $u$ and $d u$ .

$\int \cos (u) d u$

The integral of $\cos (u)$ with respect to $u$ is $\sin (u)$ .

$\sin (u) + C$

Replace all occurrences of $u$ with $\sin (x)$ .

$\sin (\sin (x)) + C$