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Find the integral of 1/x?
Integration is one of the most important concepts in calculus. Applications of integrals include finding the area under the curve, finding the values of various parameters and quantities in subjects of engineering and science. Let's solve an example related to integrals.
Answer: The integral of 1/x is ln |x| + C.
Let's understand the solution in detail.
We know that,
d/dx [ ln (x)] = 1 / x
Thus, we will do the counter process here to find the integral of 1/x.
Hence, the integral of 1/x is given by the loge|x| which is the natural logarithm of absolute x also represented as or ln |x|.
We have included the absolute value sign here around x because the logarithm of x is NOT defined for negative x values.
Also, we add an integration constant C to it if it's an indefinite integral.
By specifying the limits of the integral we can find its specific value.
☛Note: We can't use the integral identity for xn here, since ∫ xn dx = xn + 1/(n + 1) + C, and here, for 1/x, we have n = -1. Hence, ∫x-1 dx = x0/0 = undefined.
Hence, the integral of 1/x is ln |x| + C.