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.)

$Fork\ne 0,\int e^{kx}dx=\_\_\_\_\_\_\_.$

Short answer

Ans:$\int e^{kx}dx=\frac{e^{kx}}{k}+c$

Step-by-step solution

Step 1. Given information:

$$\begin{gathered} k\ne 0 \\ \int e^{kx}dx \end{gathered}$$

Step 2. Solution:

$$\begin{gathered} \int x^{k}dx=?[wherek\ne 0] \\ =\frac{e^{kx}}{k}+c \end{gathered}$$