What is the Antiderivative of Inx: Find out Here | Integral of Inx

What is the antiderivative of Inx

Antiderivative of Inx is ∫lnxdx=xlnx-x+C.

How do you find the antiderivative of Inx/Integral of Inx?

Now, let's look at the explanation of this value.
Here, we shall use the method of Integration of each part to locate the value of ∫lnx.dx:
∫udv=uv-∫vdu
Here the terms v and u are the functions of term x.
Now, let's assume that,

• u = lnx
• du.dx = 1x
• du = 1x.dx and dv = dx

Then

• ∫dv= ∫dx
• v = x

After making the required substitutions for the integration of each part for integral of In(x), we have the equation:
∫lnx.dx= (lnx).(x)- ∫(x).(1x.dx) → (lnx).(x) - ∫x.(1x.dx)
=x.lnx - ∫1.dx
=x.lnx - x+ C

What is Integration by Parts?

Calculation of the Integral of Inx uses a special integration method termed as Integration by Parts. It is generally helpful when it comes down to multiplication of two different functions together. However, it can also help in various other ways. When decoding the answer for what is the integration of Inx, you need to understand that this method also comes with higher dimensions. The formula used with this process is also extended to the functions for several variables.