# Thread: integration by reciprocal subsitution

1. ## integration by reciprocal subsitution

integrate dx/ sqrt (x^2 - x + 1) throughb reciprocal substitution

i tried solving but i was stuck in
du / u x sqrt (1-u+u ^2)

u = 1/x

2. Originally Posted by sean123
integrate dx/ sqrt (x^2 - x + 1) throughb reciprocal substitution

i tried solving but i was stuck in
du / u x sqrt (1-u+u ^2)

u = 1/x
Dear sean,

$\int{\frac{dx}{\sqrt{x^{2}-x+1}}}$

$\int{\frac{dx}{\sqrt{\left(x-\frac{1}{2}\right)^{2}-\frac{1}{4}+1}}}$

$\int{\frac{dx}{\sqrt{\left(x-\frac{1}{2}\right)^{2}+\frac{3}{4}}}}$

Now substitute $x-\frac{1}{2}=\frac{\sqrt3}{2}tanU$

See if you can do it from here. If you need more assistance please don't hesitate to reply me.

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# reciprocal subsitation

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