The given integral can be solved by the method of substitution. The substitution that will be used is
. This gives or .
This substitution absorbs the term into . Calculate the corresponding limits of the integration in terms of the new variable u.
Limits of integration for x are from 0 to 2. New variable for integration is . So the lower limit of integration in terms of new variable will be 1. Calculate the upper limit by substituting x=2.
So, the integration with this substitution becomes . Calculate this integral using the integral
Hence, the given definite integral is equal to
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