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Evaluate: int(3x^5)/(1+x^(12))dx...

Evaluate: `int(3x^5)/(1+x^(12))dx`

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`int frac{3 x^{5}}{1+x^{12}} d x `
`text { let } x^{6}=t `
`Rightarrow 6 x^{5} d x=d t `
`Rightarrow x^{5} d x=frac{d t}{6} `
`text { Now }, int frac{3 x^{5}}{1+x^{12}} d x `
`=frac{3}{6} int frac{d t}{1+t^{2}} `
`=frac{1}{2} tan ^{-1}(t)+C `
`=frac{1}{2} tan ^{-1}(x^{6})+C`
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