If `p lt 0`, then the intergral of the form `int sqrt(px^(2)+qx+r)dx` can be obtained using the formula-

If a lt 0," then "int (dx)/(sqrt(ax^(2)+bx+c)) can be evaluated using the formula-

int(px)/root(3)(qx+r)dx

int (px+q)/(sqrt(x^(2)+r^(2)))dx

Prove that the integrals of the form int_(a)^(+oo)e^(-Px)dx "and" int_(-oo)^(b)e^(Px)dx Converge for any constant P gt 0 and diverge for p lt 0 .

Integral of F(x)/(px^(2)+qx+r)sqrt(ax^(2)+bx+c)dx

Value of x in the equations px^(2) + qx+r =0 is :

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

Discuss the signs of the roots of the equation px^(2)+qx+r=0