Solve ∫ cosx/x/x^2 wrt x

$$\int \frac { \cos \frac { x } { x } } { x ^ { 2 } } d x$$

Evaluate

$$-\frac{\cos(1)}{x}+С$$

Solution Steps

Divide x by x to get 1.

$$\int \frac{\cos(1)}{x^{2}}\mathrm{d}x$$

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

$$\cos(1)\int \frac{1}{x^{2}}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int \frac{1}{x^{2}}\mathrm{d}x with -\frac{1}{x}.

$$\cos(1)\left(-\frac{1}{x}\right)$$

Simplify.

$$-\frac{\cos(1)}{x}$$

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.

$$-\frac{\cos(1)}{x}+С$$

Differentiate w.r.t. x

$$\frac{\cos(1)}{x^{2}}$$