For `x!=0,+-1`, the expression `((1/x^(2007)-1/x^(2009))/(1/x^(2008)-1/x^(2010)))` is

x^(2009) xx(1)/(x^(2008))=x

if x+(1)/(x)=1 then x^(2009)+(1)/(x^(2009))

The coefficient of x^(2012) in the expansion of (1-x)^(2008)(1+x+x^(2))^(2007), is

Evaluate the following indefinite integrals : (i) intsqrt(a^(2)-x^(2))dx (ii) int(1)/(sqrt(49+x^(2)))dx (iii) int(1)/(xsqrt(x^(6)-1))dx (iv) intsqrt((1+x)/(1-x))dx (v) intsqrt((x^(2009))/(2x^(2008)-x^(2009)))dx (vi) int(1)/(sqrt((x-4)(x-5)))dx

Evaluate the following indefinite integrals : (i) intsqrt(a^(2)-x^(2))dx (ii) int(1)/(sqrt(49+x^(2)))dx (iii) int(1)/(xsqrt(x^(6)-1))dx (iv) intsqrt((1+x)/(1-x))dx (v) intsqrt((x^(2009))/(2x^(2008)-x^(2009)))dx (vi) int(1)/(sqrt((x-4)(x-5)))dx

Solve the equation (1)/(2)log_(2007)(x^(2)+5x)=log_(2007)sqrt(x-3)

Find the number of integers 1<=x<=2010 such that the expression (x+(x+8)sqrt((x-1)/(27)))^((1)/(3))-(x+(x+8)sqrt((x-1)/(27)))^((1)/(3))