`int_0^5 (x+[x])/(e^(x-[x]))dx=alphae^-1+beta "then" (alpha+beta)^2=?`

If the value of the integral int_0^5 (x + [x])/(e^(x - [x])) dx = alphae^(-1) + beta ,where alpha, beta in R, 5alpha + 6beta = 0, and [x] denotes the greatest integer less than or equal to x, then the value of (alpha + beta )^2 is equal to :

If the integral int_(0)^(10) ([sin2pi x])/(e^(x-[x]))dx=alpha e^(-1)+beta e^(-(1)/(2))+gamma , where alpha, beta, gamma are integers and [x] denotes the greatest integer less than or equal to x, then the value of alpha+beta+gamma is equal to :

int_0^10([sin2pix])/e^(-[x]+x)dx=alphae^(-1)+betae^(-1/2)+gamma . then find alpha+beta+gamma

if int (1)/(sqrt(9-16x^(2)))dx=alpha sin ^(-1) (beta x) +c. then alpha +(1)/(beta )=

"If "int (1)/(sqrt(4x^(2)-5))dx=alpha log|x+sqrt(x^(2)-beta)|,"then "alpha+2beta is

lim_(x rarr0)(e^(alpha x)-e^(beta x))/(sin alpha x-sin beta x)=

If alpha,beta,1 are roots of x^(3)-2x^(2)-5x+6=0(alpha>1) then 3 alpha+beta=

If int _(0) ^(pi) ( sin ^(3) x) e^(- sin^(2)x)dx = alpha - (beta)/( e) int _(0)^(1) sqrt(t) e^(t) " dt , then " alpha + beta is equal to _____

int(dx)/((x-beta)sqrt((x-alpha)(beta-x))) is