Question

Integral Formulas:

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

(The last six formulas involve hyperbolic functions and their inverses.)

$Fork\ne -1,\int x^{k}dx=\_\_\_\_\_\_.$

Short answer

Ans:$\int x^{k}dx=\frac{x^{k+1}}{k+1}+c$

Step-by-step solution

Step 1. Given information:

$k\ne -1$

Step 2. Solution:

$$\begin{gathered} \int x^{k}dx=?[wherek\ne -1] \\ =\frac{x^{k+1}}{k+1}+c \end{gathered}$$