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Integrate: 1 / x^2 (1+x^4) ^3/4 .

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Solution:

$I=int frac1x^2(1+x^4)^frac34dx=int frac1x^2cdot x^3(frac1x^4+1)^frac34dx$

Put $1+frac1x^4=tRightarrow -frac4x^5dx=dt,$

$Rightarrow$ $I=-frac14 int t^-frac34dt=-frac14cdot fract^ frac14frac14+c$

$Rightarrow$ $I=-frac(1+x^4)^frac14x+c.$

Posted by

Deependra Verma

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