`int (dx)/sqrt(1-tan^2 x)=1/lambda sin^-1 (lambdasinx)+C`,then `lambda=`

int (dx)/(sqrt(1-tan ^(2) x))=(1)/(lamda)sin ^(-1) (lamda sin x)+C, then lamda=

Let J=int_(0)^(1)cot^(-1)(1-x+x^(2))dx and K= int_(0)^(1)tan^(-1)xdx .If J=lambda K (lambda in N) , then lambda equals

The complete set of values of x satisfying the inequality sin^(-1)(sin 5) gt x^(2)-4x is (2-sqrt(lambda-2pi), 2+sqrt(lambda-2pi)) , then lambda=

The complete set of values of x satisfying the inequality sin^(-1)(sin 5) gt x^(2)-4x is (2-sqrt(lambda-2pi), 2+sqrt(lambda-2pi)) , then lambda=

If int (dx)/(1+sinx) = tan (x/2 - pi/lambda) + b , then the value of lambda is -

If the equation sin(cot^(-1)(cot^(-1)(tan^(-1))))=lambda has a solution, then lambda lies in the interval a. (0,1] b. [1/(sqrt(2)),1] c. [1/(sqrt(2)),1/(sqrt(2))] d. (-oo,1]

If the equation sin(cot^(-1)(cot^(-1)(tan^(-1))))=lambda has a solution,then lambda lies in the interval a.(0,1] b.[(1)/(sqrt(2)),1] c.[(1)/(sqrt(2)),(1)/(sqrt(2))] d.(-oo,1]

If int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx=mu e^(x)((1+x)/(1-x))^(lambda)+C , then 2(lambda+mu) is equal to ..... .

If int(e^(x)(2-x^(2)))/((1-x)sqrt(1-x^(2)))dx=mu e^(x)((1+x)/(1-x))^(lambda)+C , then 2(lambda+mu) is equal to ..... .