2

We omit the constant of integration in all the formulas of this chapter. Therefore, the equality sign (=) means that the functions on the left and right of this symbol differ by a constant. For example (see integral 2.01 15), we write

$\int \frac{\text{d}x}{1+{x}^{2}}=\mathrm{arctan}x=-\text{arccot}x$

although

$\text{arctan}\text{}x\text{}=\text{}-\text{}\text{arccot}\text{}x\text{}\pm \text{}\frac{\pi}{2}$

When we integrate certain functions, we obtain the logarithm of the absolute value $(\text{for}\text{}\text{example}\text{}{\displaystyle \int \frac{\text{d}x}{\sqrt{1\text{}\text{+}\text{}{x}^{2}}}\text{}=\text{}ln\text{}\left|x\text{}\text{+}\text{}\sqrt{1\text{}+\text{}{x}^{2}}\right|}).$ In such formulas, the absolute-value ...

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