A Very Special Integral - Taking x^n Common #!#Kutur Putur Form

Integration of sin^(m)x cos^(n)xmn are integer

Integrate w.r.tx,x^(n)log x

Assertion : Fertilisation which takes place inside the female body is called internal fertilisation. Reason: Internal fertilisation is very common in aquatic animals such as starfish.

The value of the integral int_0^1 x(1-x)^n dx=

Three numbers are randomly selected from the set {10, 11, 12, ………, 100}. Probability that they form a Geometric progression with integral common ratio greater than 1 is :

For some natural N, the number of positive integral ‘x’ satisfying the equation, 1! + 2 ! + 3! + ...........+ (x!) = (N)^(2) is

If [x] denotes the integral part of x and n is a natural number such that 1<=n<100 then the number of solutions of the equation [(n)/(2)]+[(n)/(3)]+[(n)/(5)]=(n)/(2)+(n)/(3)+(n)/(5) is

Integral of form (f(x))^(n)f'(x)dx