1.

Evaluate \(\int_0^1(6x + 1) \sqrt{3x^2 +x+ x + 5dx}\)

Answer»

Put 3x2 + x + 5 = t. 

(6x + 1)dx = dt 

When x = 0 then t = 5 

When x = 1 then t = 9

\(= \frac{2}{3}(9^\frac{3}{2} - 5^\frac{3}{2}) = \frac{2}{3}(27 - 5 \sqrt5)\)



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