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 let us substitute in the given question equation






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