Integral 1+4x/ √1+x+2x^2 dx

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∫ (1 + 4x) / √(1+ x + 2x²) dx

∫ (1 +4x) (1 + x + 2x²) ^(-1/2) dx

u = 1 + x + 2x²
du = (1 + 4x) dx

= ∫ u^(-1/2) du

=  2 u^(1/2) + c

= 2 √u + c

= 2 √(1 + x + 2x²) + c