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

1.	Integrate [x+1/x]^3please solve it fast
Answer» 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

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

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

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