Evaluate I=`int [[sqrt(u)](-1/u)]^2 du`

Evaluate int (du)/(1+sinu+cosu)

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

"int(tan^(-1)u)/((1+u)^(2))du

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

If f(a)= int_(0)^(a)(du)/((1+u^(2))^(1/2)), then value of the expression 3sqrt(2)f(2sqrt(2)) is equal to "

If f(a)=int_(0)^(a)(du)/((1+u^(2))^(3/2)) , then value of the expression 3sqrt(2)f(2sqrt(2)) is equal to

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

If F(x)=int_(1)^(x) f(t) dt ,where f(t)=int_(1)^(t^(2))(sqrt(1+u^(4)))/(u) du , then the value of F''(2) equals to

int_(1)^(2)((x^(2)-1)dx)/(x^(3)*sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where u are ( in their blowest form.Find the value of )/(sqrt(2x^(4)-2x^(2)+1))=(u)/(v) where of ((1000)u)/(v)

Let vec u be a vector on rectangular coordinate system with sloping angle 60^(0). Suppose that |vec u-hat i| is geometric mean of |vec u| and |vec u-2hat i|, where hat i is the unit vector along the x-axis.Then find the value of (sqrt(2)+1)|vec u|