If ∫$$x5m$$−$$1+2x4m$$−$$1x2m+xm+13dx=f(x)+C$$ then $$f(x)=0$$

Correct option is 3x4m2mx2m+xm+12

Questions

$If \int \frac{x^{5 m - 1} + 2 x^{4 m - 1}}{{(x^{2 m} + x^{m} + 1)}^{3}} d x = f (x) + C then f (x) = 0$

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x5m2mx2m+xm+12

2m x5mx2m+xm+1

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detailed solution

Correct option is C

∫x5m−1+2x4m−1dxx6m1+1xm+1x2m3=∫x−m−1+2x−2m−1dx1+x−m+x−2m3=−1m∫dtt3 put t=1+x−m+x−2m=−1m1+x−m+x−2m−2+C=x4m2mx2m+xm+12+C

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If ∫x5m−1+2x4m−1x2m+xm+13dx=f(x)+C then f(x)=0

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Ready to Test Your Skills?

free study material

$If \int \frac{x^{5 m - 1} + 2 x^{4 m - 1}}{{(x^{2 m} + x^{m} + 1)}^{3}} d x = f (x) + C then f (x) = 0$