# How do you integrate #int4x(x^2+3)^(-3) dx#?

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To integrate ( \int 4x(x^2+3)^{-3} , dx ), perform the substitution ( u = x^2 + 3 ). Then, ( du = 2x , dx ). Rewrite the integral in terms of ( u ). The integral becomes ( \int \frac{2}{u^3} , du ). Integrate ( \frac{2}{u^3} ) with respect to ( u ) to get ( -\frac{1}{u^2} ). Finally, substitute back ( x^2 + 3 ) for ( u ) to get the final answer: ( -\frac{1}{x^2 + 3} + C ).

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