If `I_(3,8)=int x^(3)(1+x)^(8)dx=((1+x)^n)/mf(x)+C`, where f(x) is a cubic polynomial with integer coefficients, then the middle digit of m equal to

int x^8/(1+x^3)^(1//3)dx

If int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C where, C is a constant of integration, then the function f(x) is equal to

If int(dx)/(x^(3)(1+x^(6))^(2//3)) = xf(x)(1+x^(6))^(1//3)+ C Where C is a constant of inergration, then the function f(x) is equal to :-

If I=int(dx)/(x^(3)(x^(8)+1)^(3//4))=(lambda(1+x^(8))^((1)/(4)))/(x^(2))+c (where c is the constant of integration), then the value of lambda is equal to

If the integral I=inte^(x^(2))x^(3)dx=e^(x^(2))f(x)+c , where c is the constant of integration and f(1)=0 , then the value of f(2) is equal to

If I_(n)=int_(0)^( pi)e^(x)(sin x)^(n)dx, then (I_(3))/(I_(1)) is equal to

If int e^(x)((3-x^(2))/(1-2x+x^(2)))dx=e^(x)f(x)+c , (where c is constant of integration) then f(x) is equal to

If f(x) be a cubic polynomial and lim_(x rarr0)(sin^(2)x)/(f(x))=(1)/(3) then f(1) can not be equal to :

The value of int_0^1 (x^(3))/(1+x^(8))dx is

int(dx^(3))/(x^(3)(x^(n)+1)) equals