Evaluate the following definite Integrals:

For this we have to apply integration by parts

Let u and v be two functions then

To choose the first function u we use “ILATE” rule

That is

I=inverse trigonometric function

L=logarithmic function

A=algebraic function

T=trigonometric functions

E=exponential function

So in this preference, the first function is chosen to make the integration simpler.

Now, In the given question 1 is an algebraic function and it is chosen as u(A comes first in “ILATE” rule)

So first let us integrate the equation and then let us substitute the limits in it.

Let us recall that derivative of logx is 1/x

=xlogx–x

Now let us substitute the limits

= 2 log2–2–[1log1–1]

=2log2–1