Integral of $$$\cos{\left(v \right)}$$$
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Your Input
Find $$$\int \cos{\left(v \right)}\, dv$$$.
Solution
The integral of the cosine is $$$\int{\cos{\left(v \right)} d v} = \sin{\left(v \right)}$$$:
$${\color{red}{\int{\cos{\left(v \right)} d v}}} = {\color{red}{\sin{\left(v \right)}}}$$
Therefore,
$$\int{\cos{\left(v \right)} d v} = \sin{\left(v \right)}$$
Add the constant of integration:
$$\int{\cos{\left(v \right)} d v} = \sin{\left(v \right)}+C$$
Answer
$$$\int \cos{\left(v \right)}\, dv = \sin{\left(v \right)} + C$$$A
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