`int_0^1x^5(1-x)^6dx=1/lambda` then number of prime factors of `lambda` is

int_0^1x (1-x)^5 dx

int_0^5 ((1/x)-1) dx = ?

If the value of int_0^pi(x/(1+sinx))^2dx=lambda , then find the value of the integral =int_0^pi[(2x^2*cos^2(x/2))/(1+sinx)^2]dx

if I=int_0^(pi/2) dx/(5+3sinx)=lambdatan^(-1)(1/2) then value of lambda is

If int_(0)^(a)f(2a-x)dx=muandint_(0)^(a)f(x)dx=lambda , then int_(0)^(2a)f(x)dx equals a) 2lambda-mu b) lambda+mu c) mu-lambda d) lambda-2mu

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

For continuous function f: [0, 1]-> R ; A =int_0^1 (x^2* f(x))dx ; B=int_0^1 x * (f(x))^2 dx then, maximumvalue of A-B is lambda where [1/(4lambda)] is

If alpha, beta are the roots of the equation lambda(x^(2)-x)+x+5=0 and if lambda_(1) and lambda_(2) are two values of lambda obtained from (alpha)/(beta)+(beta)/(alpha)=(4)/(5) , then (lambda_(1))/(lambda_(2)^(2))+(lambda_(2))/(lambda_(1)^(2)) equals

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

If the integral int_(sin^(-1)(sin8))^(tan^(-1)(tan8))(sin^(3)(x^(5))+sin^(5)(x^(3)))/(cos^(6)x+cos^(8)x)dx has the value lambda ; then the least prime number greater than lambda is