`(x^(n-1))/(sqrt(1+4x^(n)))`

(b) int(x^(n-1)dx)/(sqrt(a^n+x^n))

If I_(n)=int(x^(n)dx)/(sqrt(x^(2)+a)) then prove that I_(n)+(n-1)/(n)al_(n-2)=(1)/(n)x^(n-1)*sqrt(x^(2)+a)

int_(0)^(1)((3x^(2))/(sqrt(1-x^(6)))+(4x^(3))/(sqrt(1-x^(8)))+(5x^(4))/(sqrt(1-x^(10)))+...." to "n" terms ")dx=

int(e^(x)(1-nx^(n-1)-x^(2n)))/((1-x^(n)) sqrt(1-x^(2n)))d=....+c

Evaluate: int e^(x)(1+nx^(n-1)-x^(2n))/((1-x^(n))sqrt(1-x^(2n)))dx

int(x^(n-1)dx)/( sqrt(a^(n)+x^(n)))

If f(x)=lim_(n rarr oo)(x^(n)-x^(-n))/(x^(n)+x^(-n)),x>1 then int(xf(x)log(x+sqrt(1+x^(2))))/(sqrt(1+x^(2)))dx is

Integrate the following w.r.t. x: frac {x^(n-1)}{ sqrt (1+ 4 x^n)}

If quad sqrt(3) and x_(n+1)=(x_(n))/(1+sqrt(1+x_(n)^(2))),AA n in N then lim_(n rarr oo)2^(n)x_(n) is equal to ,AA n in N