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If $\int \frac{x^{7}}{{(1 + x^{4})}^{2}} d x = \frac{1}{4} [\log (1 + x^{4}) + f (x)] + C$ then

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f(x)=1+x4

f(x)=11+x42

f(x)=11+x4

f(x)=tan−1⁡1+x4

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detailed solution

Correct option is C

Put 1+x4=t , so that ∫x71+x42dx=14∫(t−1)t2dt=14log⁡|t|+141t+C=14log⁡1+x4+11+x4+C∴f(x)=11+x4

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If ∫x71+x42dx=14log⁡1+x4+f(x)+C then

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If $\int \frac{x^{7}}{{(1 + x^{4})}^{2}} d x = \frac{1}{4} [\log (1 + x^{4}) + f (x)] + C$ then