x^(ln)*int(int_(0)^(x)sin^(2)t cos t)/(x^(3))d

lim_ (x rarr0) (int_ (0) ^ (x) sin ^ (2) t cos tdt) / (x ^ (3))

Lt_ (x rarr0) ((int_ (0) ^ (x) sin ^ (3) t cos tdt) / (x ^ (4)))

If f(x)=int_(0)^(x)(sin^(4)t+cos^(4)t)dt, then f(x+pi) will be equal to

If int_(y)^(y)cos t^(2)dt=int_(0)^(x^(2))(sin t)/(t)dx, the prove that (dy)/(dx)=(2sin x^(2))/(x cos y^(2))

If x satisfies the equation x^(2)(int_(0)^( pi/2)(2sin t+3cos t)dt)-x(int_(-3)^(3)(t^(2)sin2t)/(t^(2)+1))-2=0 ,then the value of x is

lim_( x to 0) ( int_(0)^(x^(2)) cos^(2)t" "dt)/(x sin x) = ...

If int_(0)^(y)cos t^(2)dt=int_(0)^(x^(2))(sin t)/(t)dt, then (dy)/(dx) is

A function f is continuous for all x (and not everywhere zero) such that f^(2)(x)=int_(0)^(x)f(t)(cos t)/(2+sin t)dt. Then f(x) is (1)/(2)ln((x+cos x)/(2));x!=0(1)/(2)1n((3)/(x+cos x));x!=0(1)/(2)ln((2+sin x)/(2));x!=n pi,n in I(cos x+sin x)/(2+sin x);x!=n pi+(3 pi)/(4),n in I