Evaluate the following definite Integrals:

Since it is a quadratic equation we are trying to make it a complete square

=here the equation is in the form of integral of the integral is equal to

Here let us assume that t=x–

So that dx=dt

When x=0 t=–1/2

And when x=–1/2, t=3/2

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]

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Now rationalize the denominator

We get as