| Table of Infinite Integrals Continues | |
|---|---|
| 27 Integrals Component $ e^{ax} $ | |
| $ \int e^{ax}dx=\frac{e^{ax}}{a} $ | |
| $ \int x e^{ax}dx=\frac{e^{ax}}{a}\left(x-\frac{1}{a} \right) $ | |
| $ \int x^2 e^{ax}dx=\frac{e^{ax}}{a}\left(x^2-\frac{2x}{a}+\frac{2}{a^2}\right) $ | |
| $ \int x^n e^{ax}dx=\frac{x^n e^{ax}}{a}-\frac{n}{a} \int x^{n-1} e^{ax}dx = \frac {e^{ax}}{a} \left( x^n- \frac{nx^{n-1}}{a}+\frac{n(n-1)x^{n-2}}{a^2}- \cdot \cdot \cdot \frac{(-1)^n n!}{a^n} \right ) \qquad \text{if n is a poaitive integer} $ | |
