∫ 1/x dx
The given notation ∫ 1/x dx represents an indefinite integral of the function 1/x with respect to the variable x
The given notation ∫ 1/x dx represents an indefinite integral of the function 1/x with respect to the variable x. This integral signifies finding the antiderivative of the function 1/x.
To solve this integral, we can use the property of logarithms. The integral of a function of the form 1/x can be expressed as the natural logarithm of the absolute value of x, plus a constant of integration.
∫ 1/x dx = ln |x| + C
Here, ln |x| represents the natural logarithm of the absolute value of x, and C represents the constant of integration. The absolute value is included to handle both positive and negative values of x since the natural logarithm is only defined for positive values.
So, the solution to the integral ∫ 1/x dx is ln |x| + C.
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