Question

Integral Formulas: Fill in the blanks to complete each of the following integration formulas.

$\int sec{\mathrm{h}}^{2}xdx=...$

Short answer

The value of$\int sec{\mathrm{h}}^{2}xdx=\tanh x+\mathrm{C}$.

Step-by-step solution

Step 1. Given information.

Consider the given integral function$\int sec{\mathrm{h}}^{2}xdx$.

Step 2. Fill the blank for the integral function ∫sech2xdx.

The theorem of Integrals of Hyperbolic Functions states that $\int sec{\mathrm{h}}^{2}xdx=\tanh x+\mathrm{C}$.

Therefore, it can be said the appropriate fill in black will be$\int sec{\mathrm{h}}^{2}xdx=\tanh x+\mathrm{C}$.