Solve ∫ cosxcosy wrt y

$$\int \cos x \cos y d y$$

Evaluate

$$\sin(y)\cos(x)+С$$

Solution Steps

Factor out the constant using \int af\left(y\right)\mathrm{d}y=a\int f\left(y\right)\mathrm{d}y.

$$\cos(x)\int \cos(y)\mathrm{d}y$$

Use \int \cos(x)\mathrm{d}x=\sin(x) from the table of common integrals to obtain the result.

$$\cos(x)\sin(y)$$

If F\left(y\right) is an antiderivative of f\left(y\right), then the set of all antiderivatives of f\left(y\right) is given by F\left(y\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\cos(x)\sin(y)+С$$

Differentiate w.r.t. x

$$-\sin(x)\sin(y)$$