Question

Write out all the integration formulas and rules that we know at this point.

Short answer

The formulas are:

$$\begin{gathered} \int x^{k}dx=\frac{1}{k+1}{x}^{k+1}+C \\ \int \frac{1}{x}dx=\ln \left|x\right|+C \\ \int e^{kx}dx=\frac{1}{k}{e}^{kx}+C \\ \int b^{x}dx=\frac{1}{\ln b}{b}^x+C \\ \int \sin xdx=-\cos x+C \end{gathered}$$

Step-by-step solution

Step 1. Given information.

According to the question, we need to write all the integral formulas.

Step 2. Explanation.

The formulas that are known so far are:

$$\begin{gathered} \int x^{k}dx=\frac{1}{k+1}{x}^{k+1}+C\{Powerfunction\} \\ \int \frac{1}{x}dx=\ln \left|x\right|+C \\ \int e^{kx}dx=\frac{1}{k}{e}^{kx}+C\{Exponentialfunction\} \\ \int b^{x}dx=\frac{1}{\ln b}{b}^x+C \\ \int \sin xdx=-\cos x+C\{TrignometricFunction\} \end{gathered}$$