The integrals below involve `x^4+-a^4`
1) `int 1/(x^4+a^4) dx = 1/(4a^3sqrt2) ln ((x^2+axsqrt2+a^2)/(x^2-axsqrt2+a^2))-1/(2a^3sqrt2) tan^-1((axsqrt2)/(x^2-a^2))`
2) `int x/(x^4+a^4) dx = 1/(2a^2) tan^-1(x^2/a^2)`
3) `int x^2/(x^4+a^4) dx = 1/(4asqrt2) ln ((x^2-axsqrt2+a^2)/(x^2+axsqrt2+a^2))-1/(2asqrt2) tan^-1((axsqrt2)/(x^2-a^2))`
4) `int x^3/(x^4+a^4) dx = 1/4 ln (x^4+a^4)`
5) `int 1/(x(x^4+a^4)) dx = 1/(4a^4) ln (x^4/(x^4+a^4))`
6) `int 1/(x^2(x^4+a^4)) dx = -1/(a^4x)-1/(4a^5sqrt2) ln ((x^2-axsqrt2+a^2)/(x^2+axsqrt2+a^2))+1/(2a^5sqrt2) tan^-1((axsqrt2)/(x^2-a^2))`
7) `int 1/(x^3(x^4+a^4)) dx = -1/(2a^4x^2)-1/(2a^6) tan^-1 (x^2/a^2)`
8) `int 1/(x^4-a^4) dx = 1/(4a^3) ln ((x-a)/(x+a))-1/(2a^3) tan^-1(x/a)`
9) `int x/(x^4-a^4) dx = 1/(4a^2) ln ((x^2-a^2)/(x^2+a^2))`
10) `int x^2/(x^4-a^4) dx = 1/(4a) ln ((x-a)/(x+a))+1/(2a) tan^-1(x/a)`
11) `int x^3/(x^4-a^4) dx = 1/4 ln (x^4-a^4)`
12) `int 1/(x(x^4-a^4)) dx = 1/(4a^4) ln ((x^4-a^4)/x^4)`
13) `int 1/(x^2(x^4-a^4)) dx = 1/(a^4x)+1/(4a^5) ln((x-a)/(x+a))+1/(2a^5) tan^-1(x/a)`
14) `int 1/(x^3(x^4-a^4)) dx = 1/(2a^4x^2)+1/(4a^6) ln ((x^2-a^2)/(x^2+a^2))`