MathLiveIntegral of the reciprocal function
This gives the antiderivative of 1/x for x not equal to zero, which is the natural logarithm of the absolute value of x plus a constant. The absolute value makes the formula valid on both sides of zero, where separate constants of integration apply. It is also the basis for integrating 1/(ax+b) by substitution and for logarithmic terms in partial fraction decompositions with linear denominators.
\int \frac{1}{x}\,dx = \ln\left|x\right| + CWhat the symbols mean
| the variable of integration (nonzero real number) | |
| constant of integration |
About this formula
- FieldMathematics
- TopicIntegral calculus
- LevelHigh school
- Also calledintegral of 1/x, antiderivative of 1/x, natural logarithm integral, integral of one over x, log integral, integral of reciprocal
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