integral (X^2-1/X^2)^2 dx

semoga membantu dan bermanfaat
[tex] \int\limits^ {}( x^{2} - \frac{1}{ x^{2} }) ^{2} \, dx [/tex]
gunakan aturan [tex](a-b) ^{2} = a^{2}-2ab+ b^{2} [/tex]
[tex]=( x^{2} )^{2} - 2 x^{2} \frac{1}{ x^{2} }+ (\frac{1}{ x^{2} } ) ^{2} = x^{4}-2+ \frac{1}{ x^{4} } [/tex]
[tex] \int\limits^{}f(x)-g(x) \, dx= \int\limits^{}f(x) \, dx - \int\limits^{}g(x) \, dx [/tex]
[tex] \int\limits^{} x^{4}-2+ \frac{1}{ x^{4} } \, dx= \int\limits^{}x^{4} \, dx - \int\limits^ {}2 \, dx + \int\limits^ {} \frac{1}{ x^{4} } \, dx [/tex]
[tex] \int\limits^ {}x ^{a} \, dx = \frac{ x^{a+1} }{a+1} [/tex]
[tex] \int\limits^ {}x^{4} \, dx= \frac{ x^{4+1} }{4+1}= \frac{ x^{5} }{5} [/tex]
[tex] \int\limits^{}a \, dx=ax [/tex]
[tex] \int\limits^ {}2 \, dx =2x[/tex]
[tex] \int\limits^ {} \frac{1}{ x^{4} } \, dx= \int\limits^ {} x^{-4} \, dx= \frac{ x^{-4+1} }{-4+1}= \frac{x^{-3} }{-3}= -\frac{1}{3x^{3} } [/tex]
[tex]= \frac{ x^{5} }{5}-2x- \frac{1}{3 x^{3} }+C [/tex]