Solve int ∫ (from cos ( 16 pi x ) to 5) of wrt ydx

$$\int \int _ { \cos ( 16 \pi x ) } ^ { 5 } d y d x$$

Evaluate

$$-\frac{\sin(16\pi x)}{16\pi }+5x+С$$

Solution Steps

Simplify.

$$5x-\cos(16\pi x)x+\frac{x\cos(16x\pi )\pi -\frac{\sin(16x\pi )}{16}}{\pi }$$

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.

$$5x-\cos(16\pi x)x+\frac{x\cos(16x\pi )\pi -\frac{\sin(16x\pi )}{16}}{\pi }+С$$

Differentiate w.r.t. x

$$-\cos(16\pi x)+5$$