Calculate the integral.
The form of the given indefinite integral resembles the form of .
Thus we should consider a u-substitution that changes to .
Such a substitution is
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Find du.
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
Substitute and into so that the integrand is rewritten in terms of u only. We will first choose to use the simple algebraic manipulation of multiplying the numerator and denominator of the integrand by x so we can substitute .
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
Since is never less than 0, we have . Use this fact to integrate with respect to u. (Use C for the constant of integration.)
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
Use the substitution to write in terms of x to calculate the indefinite integral. (Use C for the constant of integration.)
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