Difficult integrate: ∫√(x^2+x) dx

JeisonJoe

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Oct 1, 2016
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Hello, I need help with this integrate:

clip_image002.png

∫√(x^2+x) dx


thanks.
 
Hello, I need help with this integrate:

clip_image002.png

∫√(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...
 
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Hello, I need help with this integrate:

clip_image002.png

∫√(x^2+x) dx

For future reference, please note that we have no (legal) way of viewing files from your own computer. If an image is necessary, kindly please follow the instructions for clicking the button to post such. (here). Thank you! ;)
 
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.
 
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