A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
How to integrate ln x/x?
To find Integration of ln x/x, we will use the substitution rule for integration.
Answer: The final integral of ln x/x is (1/2) ln(x)2 + c.
Go through the explanation to understand better.
Explanation:
Given:
y = ln x/x
y = (1/x)ln x
Now, we have the two functions;
f(x) = 1/x --------------- (1)
g(x) = ln(x) ------------- (2)
We know that the derivative of ln(x) is (1/x), so f(x) = g'(x).
We have to use integration by substitution to solve the original equation.
Let u = ln(x) ------------- (3)
du/dx = 1/x
du = (1/x)dx --------------- (4)
Substituting from equations (1), (2), (3) and (4) in the original integral we get,
∫ ln(x) (1/x) dx = ∫u du = (1/2) u2 + c
Re-substituting for u gives us;
= (1/2) ln(x)2 + c
Thus, the final integral of ln x/x is (1/2) ln(x)2 + c.
Math worksheets and
visual curriculum
visual curriculum