# How do you use substitution to integrate #(5x+10)/(3x^(2) +12x - 7)#?

Start by factoring the 5 out of the numerator.

And reversing the substitution gets us

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To integrate ( \frac{5x + 10}{3x^2 + 12x - 7} ) using substitution, let ( u = 3x^2 + 12x - 7 ). Then, find ( du ) by differentiating ( u ) with respect to ( x ). After finding ( du ), express ( \frac{5x + 10}{3x^2 + 12x - 7} ) in terms of ( u ) and ( du ). This will transform the integral into a simpler form that can be integrated more easily. Finally, integrate the expression in terms of ( u ), and substitute back the original variable ( x ) to obtain the final result.

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