Solve ∫ operatorname{arccosec}(x) wrt x

$$\int \operatorname { arccosec } ( x ) d x$$

Evaluate

$$\frac{x^{2}\arccos(ec)}{2}+С$$

Solution Steps

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

$$\arccos(ec)\int x\mathrm{d}x$$

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

$$\arccos(ec)\times \frac{x^{2}}{2}$$

Simplify.

$$\frac{\arccos(ec)x^{2}}{2}$$

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.

$$\frac{\arccos(ec)x^{2}}{2}+С$$

Differentiate w.r.t. x

$$x\arccos(ec)$$