`int (2x^(n-1))/(x^n+3) `dx

The value of ("^n C_0)/n + ("^nC_1)/(n+1) + ("^nC_2)/(n+2) +....+ ("^nC_ n)/(2n) is equal to a. int_0^1x^(n-1)(1-x)^n dx b. int_1^2x^n(x-1)^(n-1)dx c. int_1^2x^(n-1)(1+x)^n dx d. int_0^1(1-x)^(n-1)dx

Evaluate int(x^(2)+n(n-1))/((x sin x + n cos x)^(2))dx .

if int (1+x^n)^(1/n)/x^(n+2)dx = a(1+1/x^4)^b+c then value of a+b=

The value of (.^(n)C_(0))/(n)+(.^(n)C_(1))/(n+1)+(.^(n)C_(2))/(n+2)+"..."+(.^(n)C_(n))/(2n) (a) underset(0)overset(1)intx^(n-1)(1+x)^(n)dx (b) underset(1)overset(2)intx^(n)(x-1)^(n-1)dx (c) underset(1)overset(2)int(1+x)^(n)dx (d) underset(0)overset(1)int(1-x)^(n)x^(n-1)dx

Connect int x^(m-1)(a+bx^(n))^(p)dx with int x^(m-n-1)(a+bx^(n))^(p)dx and evaluate int(x^(8)dx)/((1-x^(3))^(1//3)) .

IfI(m , n)=int_0^1x^(m-1)(1-x)^(n-1)dx ,(m , n in I ,m ,ngeq0),t h e n (a) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m-n))dx (b) I(m , n)=int_0^oo(x^(m-1))/((1+x)^(m+n))dx (c) I(m , n)=int_0^oo(x^(n-1))/((1+x)^(m+n))dx (d) I(m , n)=int_0^oo(x^n)/((1+x)^(m+n))dx

If n in N , then int_(-n)^(n)(-1)^([x]) dx equals

Let m,n be two positive real numbers and define f(n)=int_(0)^(oo)x^(n-1)e^(-x)dx and g(m,n)=int_(0)^(1)x^(m-1)(1-x)^(n-1)dx . It is known that f(n) for n gt 0 is finite and g(m, n) = g(n, m) for m, n gt 0 . int_(0)^(1)(x^(m-1)+x^(n-1))/((1+x)^(m+n))dx=

Evaluate : int_(0)^(1)x(1-x)^(n)dx

If I(m,n)=int_0^1x^(m-1)(1-x)^(n-1)dx , then