∫ 1/x dx
To solve the integral of 1/x, we need to consider different cases
To solve the integral of 1/x, we need to consider different cases.
Case 1: Integration of 1/x when x is greater than 0.
In this case, we can use the natural logarithm function.
∫ (1/x) dx = ln |x| + C
Here, the absolute value bars are used because the natural logarithm is only defined for positive values of x, and we need to include both positive and negative values of x in the original integral.
Case 2: Integration of 1/x when x is less than 0.
In this case, we need to consider the absolute value of x:
∫ (1/x) dx = ln |-x| + C
= ln |x| + C
Since the absolute value of -x is the same as the absolute value of x, we can express the integral as ln |x| + C in both cases.
Therefore, the indefinite integral of 1/x is ln |x| + C, where C is the constant of integration.
More Answers:
Understanding the Integration of sec²(x) using Trigonometric Identity and Power RuleHow to Integrate sec(x) tan(x) with respect to x? A Step-by-Step Guide
How to Find the Integral of 1/(x^2 + 1) dx Step by Step with Partial Fraction Decomposition and Substitution