Integral of $$$\cos{\left(x^{5} \right)}$$$ with respect to $$$z$$$

Find $$$\int \cos{\left(x^{5} \right)}\, dz$$$.

Apply the constant rule $$$\int c\, dz = c z$$$ with $$$c=\cos{\left(x^{5} \right)}$$$:

$${\color{red}{\int{\cos{\left(x^{5} \right)} d z}}} = {\color{red}{z \cos{\left(x^{5} \right)}}}$$

Therefore,

$$\int{\cos{\left(x^{5} \right)} d z} = z \cos{\left(x^{5} \right)}$$

Add the constant of integration:

$$\int{\cos{\left(x^{5} \right)} d z} = z \cos{\left(x^{5} \right)}+C$$

$$$\int \cos{\left(x^{5} \right)}\, dz = z \cos{\left(x^{5} \right)} + C$$$A