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Find:\(\int\frac{(6x^2-6x+5)dx}{\sqrt{2x^3-3x^2+5x-7}}\)Integrate (6x2 - 6x + 5)/(√(2x3 - 3x2 + 5x - 7) |
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Answer» Let I = \(\int\frac{(6x^2-6x+5)dx}{\sqrt{2x^3-3x^2+5x-7}}\) Let 2x3 - 3x2 + 5x - 7 = t ⇒ (6x2 - 6x + 5)dx = dt \(\therefore\) I = \(\int\frac{dt}{\sqrt t}=2t^{1/2} + c\) Hence, \(\int\frac{(6x^2-6x+5)dx}{\sqrt{2x^3-3x^2+5x-7}}\) = \(2\sqrt{2x^3-3x^2+5x-7}+c\). |
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