`int_(2)^(3)u sqrt(5-u)du`

If int_(0)^(x){int_(0)^(u)f(t)dx}du is equal to (a)int_(0)^(x)(x-u)f(u)(b)int_(0)^(x)uf(x-u)du(c)x int_(0)^(x)f(u)du(d)x int_(0)^(x)uf(u-x)du

int(1)/(sqrt(u))du

If variables x and y are related by the equation x=int_(0)^(y)(1)/(sqrt(1+9u^(2))) du, then (dy)/(dx) is equal to

If variables x and y are related by the equation x=int_(0)^(y)(1)/(sqrt(1+9u^(2))) du, then (dy)/(dx) is equal to

if int_(log2)^(x) (du)/(e^u-1)^(1/2) =pi/6 then e^x=

if int_(log2)^(x) (du)/(e^u-1)^(1/2) =pi/6 then e^x=

Let f(u) be a continuous function and for any real number u.let [ul denote the greatest integer less than or equal to u.Show that for any x>1int_(1)^(x)[u]([u]+1)f(u)du=2sum_(i=1)^(x)i int_(i)^(x)f(u)du

int (du) / (u sqrt (u ^ (2) -1))