Evaluate the definite integral.

You need to solve the definite integral, using fundamental theorem of calculus, such that:

First, you need to solve the indefinite integral , using parts, such that:

If yields:

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You need to solve the definite integral, using fundamental theorem of calculus, such that:

First, you need to solve the indefinite integral , using parts, such that:

If yields:

Using parts again for yields:

Using parts again for  yields:

Using parts for the last time for  yields:

Take the result and replace it for above:

Take the result  and replace it for  above:

Take the result  and replace it for  above:

Calculating the integral yields:

Reducing like terms yields:

You also may solve the integral by noticing the the function is odd and you may use the propert if f(x) is odd.

You may prove that is odd such that:

Hence, evaluating the definite integral, using either the fundamental theorem of calculus, or the property of odd functions  , yields