integration 1

âˆ«dxx+âˆšx²-x+1

2 Answers

106

Asish Mahapatra ·2009-12-04 00:09:07

rationalise it

ull get âˆ«x-√x²-x+1x-1

now splitting u get,

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

=\int \frac{x-1}{x-1}+1/(x-1)+\frac{x^2-x}{(x-1)\sqrt{x^2-x+1}}+\frac{1}{(x-1)\sqrt{x^2-x+1}}dx

=\int \1+1/(x-1)+\frac{x}{(x-1)\sqrt{x^2-x+1}}+\frac{1}{(x-1)\sqrt{x^2-x+1}}dx

this can be easily solved now

substitute âˆšx²-x+1 =tx-1 [1]

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