Integral of ln2x | How to Integrate of ln2x

The integral of ln2x is equal to x(ln2x−1)+C where C is a constant. Here, we will learn how to integrate ln2x.

The integration of ln(2x) is given as follows:

∫ln2x dx = x(ln2x−1)+C
Integral of ln2x

Integration of ln2x

Question: What is the integration of ln2x?


To find the integration of ln2x, we will use the integration by parts formula. This formula is used to find the integral of the product uv, where u and v are two functions of x.

Integration by parts formula:
∫uv dx = u ∫v dx – ∫[$\frac{du}{dx}$∫v dx] dx.

Put u=ln2x and v=1.


∫ln(2x) dx = ∫ (ln2x ⋅ 1) dx

= ln2x ∫1 dx – ∫ $\big[\dfrac{d}{dx}(\ln 2x) \int 1\ dx \big]dx$

= $\ln 2x \times x -\int \big[\dfrac{1}{x} \times x \big]dx$ + C, as the derivative of ln2x is 1/x.

= x ln2x – ∫dx + C

= x ln2x – x + C

= x (ln2x – 1) + C.

So the integral of ln2x using integration by parts is equal to ∫ln2x dx = x(ln2x – 1) +C where C denotes an arbitrary integration constant.

More Integrals:

Integral of ln(x)

How to integrate sin3x

Integration of natural log of x

Integration of $\frac{x}{1+x^2}$


Q1: What is the integral of ln(2x)?

Answer: The integral of ln(2x) is equal to x(ln2x−1)+C where C is a constant.

Q2: What is ∫ln2x dx?

Answer: ∫ln2x dx = x(ln2x−1)+C.

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