Question

integrate
[x+1/x]^3
please solve it fast

Answer 1

Answer:

Step-by-step explanation:I think you mean ∫[x+(1/x)]³ dx=∫f(x)dx ,for which you have no choice but to expand the INTEGRAND in the smart way...

① f(x)=[x+(1/x)]³

=[(x²+1)/x]³

=(1+x²)³/x³

={1+3x²+3x^4+x^6}/x³

=x^(-3)+3[x^(-1)]+3x+x³

② ∫f(x)dx

=-½(1/x²)+3㏑|x|+3(x²/2)+¼x^4+C