Difficult integrate: ∫√(x^2+x) dx

[JeisonJoe]

Hello, I need help with this integrate:

∫√(x^2+x) dx


thanks.

 

[Deleted member 4993]

Hello, I need help with this integrate:

∫√(x^2+x) dx


thanks.

x^2 + x = (x + 1/2)^2 - (1/2)^2

Then substitute

1/2 * sec(Θ) = 1/2 + x

and continue...

 

[stapel]

Hello, I need help with this integrate:

∫√(x^2+x) dx

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[SAMUELK]

Complete the square.

x^2 + x = (x + 1/2)^2 - (1/2)^2

Then substitute

1/2 * sec(Θ) = 1/2 + x

and continue...

More generally, a quadratic inside a square root can be handled by completing the square, followed by a trig-substitution.