If `alpha=int_(2)^(3) (2xdx)/(x^2+1)`, then find the value of `e^alpha`

If the sum of the coefficient in the expansion of (alpha^(2)x^(2)-2 alpha x+1)^(51) vanishes,then find the value of alpha

If alpha is nonreal and alpha=(1)^((1)/(5)) then the find the value of 2^(|1+alpha+alpha^(2)+alpha^(-2)-alpha^(-2))-alpha^(-1)|

if ""_1=int_(-a)^(2a)(xdx)/(x^2+p^2),I_2=int_a^(2a)(xdx)/(x^2+p^2) then find the value of (12)/pi(I_1-I_2)

If alpha and beta are zeroes of the quadratic polynomial f(x) =3x^(2)-5x-2 , then find the value of ((alpha^(2))/(beta)+(beta^(2))/(alpha))+6(alpha+1)(beta+1) .

If alpha and beta are zeroes of the quadratic polynomial p(x)=6x^(2)+x-1, then find the value of (alpha)/(beta)+(beta)/(alpha)+2((1)/(alpha)+(1)/(beta))+3 alpha beta

If alpha be a root of equation x^2+x+1=0 then find the vlaue of (alpha+ 1/alpha)+(alpha^2+1/alpha^2)^2+(alpha^3+1/alpha^3)^2+…+(alpha^6+1/alpha^6)^2

Evaluate int_(0)^(1)(xdx)/(3+4x+x^(2))

tan(alpha+beta)=(1)/(2),tan(alpha-beta)=(1)/(3), then find the value of tan2 alpha

|[(1+alpha)^(2),(1+2 alpha)^(2),(1+3 alpha)^(2)(2+alpha)^(2),(2+2 alpha)^(2),(2+3 alpha)^(2)(3+alpha)^(2),(3+2 alpha)^(2),(3+3 alpha)^(2) Find the value of alpha

If alpha_(1),alpha_(2),alpha_(3),alpha_(4) are the roots of the equation x^(4)+(2-sqrt(3))x^(2)+2+sqrt(3)=0 then find the value of (1-alpha_(1))(1-alpha_(2))(1-alpha_(3))(1-alpha_(4))