Integral of cos(1)*cos(x)

The calculator will find the integral/antiderivative of $$$\cos{\left(1 \right)} \cos{\left(x \right)}$$$, with steps shown.

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Find $$$\int \cos{\left(1 \right)} \cos{\left(x \right)}\, dx$$$.

The trigonometric functions expect the argument in radians. To enter the argument in degrees, multiply it by pi/180, e.g. write 45° as 45*pi/180, or use the appropriate function adding 'd', e.g. write sin(45°) as sind(45).

Solution

Apply the constant multiple rule $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ with $$$c=\cos{\left(1 \right)}$$$ and $$$f{\left(x \right)} = \cos{\left(x \right)}$$$:

$${\color{red}{\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x}}} = {\color{red}{\cos{\left(1 \right)} \int{\cos{\left(x \right)} d x}}}$$

The integral of the cosine is $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:

$$\cos{\left(1 \right)} {\color{red}{\int{\cos{\left(x \right)} d x}}} = \cos{\left(1 \right)} {\color{red}{\sin{\left(x \right)}}}$$

Therefore,

$$\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x} = \sin{\left(x \right)} \cos{\left(1 \right)}$$

Add the constant of integration:

$$\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x} = \sin{\left(x \right)} \cos{\left(1 \right)}+C$$

Answer

$$$\int \cos{\left(1 \right)} \cos{\left(x \right)}\, dx = \sin{\left(x \right)} \cos{\left(1 \right)} + C$$$A

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Integral of $$$\cos{\left(1 \right)} \cos{\left(x \right)}$$$

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Solution

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