Solve ∫ 3picos(x) wrt x

$$\int{ 3 \pi \cos ( x ) }d x$$

Evaluate

$$3\pi \sin(x)+С$$

Solution Steps

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

$$3\pi \int \cos(x)\mathrm{d}x$$

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

$$3\pi \sin(x)$$

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

$$3\pi \sin(x)+С$$

Differentiate w.r.t. x

$$3\pi \cos(x)$$