Solve ∫ cosx/cos(x-a) wrt x

$$\int \frac { \cos x } { \cos ( x - a ) } d x$$

Evaluate

$$\frac{\sin(a)\cos(x-a)\ln(|\cos(x-a)|)+x\sin(a)\sin(x-a)+x\cos(x)}{\cos(x-a)}+С$$

Solution Steps

Simplify.

$$\frac{\cos(x)x}{\cos(x-a)}+\sin(a)\left(\frac{x\sin(x-a)}{\cos(x-a)}+\ln(|\cos(x-a)|)\right)$$

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.

$$\frac{\cos(x)x}{\cos(x-a)}+\sin(a)\left(\frac{x\sin(x-a)}{\cos(x-a)}+\ln(|\cos(x-a)|)\right)+С$$

Differentiate w.r.t. x

$$\frac{\cos(x)}{\cos(x-a)}$$