Q. 493.7( 3 Votes )

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Answer :

First split the integral


Now integrate by parts the first one


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 x2 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.


Remember and







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