Evaluate:`int sin^(2)u cos^(2)u du`

The number of ordered 5 -tuple (u,v,w,x,y) where (u,v,w,x,y in[1,11]) which satisfy the inequality 2^(sin^(2)u+3cos^(2)v)*3^(sin^(2)w+cos^(2)x)*5^(cos^(2)y)>=720 is

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

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

If u and v are two functions of x then prove that : int uv dx = u int v dx - int [ (du)/(dx) int v dx ] dx Hence, evaluate int x e^(x) dx

If : sin^(4)theta+cos^(4)theta+sin^(2)theta*cos^(2)theta=1-u^(2), "then" : u=

Lim_(x rarr0)int_(0)^(x)(sin^(2)u du)/(sin x)

If u_(n) = sin ^(n) theta + cos ^(n) theta, then 2 u_(6) -3 u_(4) is equal to

The length of the latus rectum of the parabola whose focus is ((u^(2))/(2g)sin2 alpha,-(u^(2))/(2g)cos2 alpha) and directrix is y=(u^(2))/(2g) is (u^(2))/(g)cos^(2)alpha(b)(u^(2))/(g)cos^(2)2 alpha(2u^(2))/(g)cos^(2)2 alpha(d)(2u^(2))/(g)cos^(2)alpha

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