hot to integrate the following:

(x10 - 1) divided by (x - 1)

the given integral is x10-1x-1.dx
=(x-1)(x9+x8+x7+x6+x5+x4+x3+x2+x+1)x-1.dx=(x9+x8+x7+x6+x5+x4+x3+x2+x+1).dx=x1010+x99+x88+x77+x66+x55+x44+x33+x22+x+Cwhere C is an integration constant.

hope this  helps you

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x raise to power n - y raise to power n [xn-yn]

=(x-y) (x raise to power n-1 + x raise to power n-2 . y +...............+ y raise to power n-1)

x10-1 = (x-1) ( x9 + x8+................+1)

now (x-1) will be cancelled from (x-1)

and the answer will be the remaining part

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