1.

Find:\(\int\frac{(6x^2-6x+5)dx}{\sqrt{2x^3-3x^2+5x-7}}\)Integrate (6x2 - 6x + 5)/(√(2x3 - 3x2 + 5x - 7)

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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