`intdx/(x^2+1)^4`

intdx/(x^2+1)^2

intdx/(x^3-1)

intdx/(e^x-1)

intdx/(x^4-a^4)

intdx/(e^x-1)^2

intdx/(x^(1/2)+x^(1/3)+x^(2/3))

intdx/((x^2-1)sqrt(x^2+1))

intdx/(x(x^5 + 1))

intdx/((x-1)^(3/4)(x+2)^(5/4))= (A) 4/3((x-1)/(x+2))^(1/4)+c (B) 4/3sqrt((x-1)/(x+2))+c (C) 4/3((x+2)/(x-1))^(1/4)+c (D) none of these

If I_n=intdx/(x^2+a^2)^n,ninN , then show that: I_(n+1)=1/(2na^2)x/((x^2+a^2)^n)+(2n-1)/(2n). 1/a^2I_n