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$If \int \frac{1 - x^{7}}{x (1 + x^{7})} d x = a \ln | x | + b \ln |x^{7} + 1| + c, then$

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a=1, b=27

a=-1, b=27

a=1, b=-27

a=-1, b=-27

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detailed solution

Correct option is C

I=∫1−x7x1+x7dx=aln⁡|x|+bln⁡1+x7+C Differentiating both sides, we get 1−x7x1+x7=ax+b⋅7x61+x7⇒ 1−x7=a1+x7+7bx7⇒ a=1,a+7b=−1⇒ b=−27

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If ∫1−x7x1+x7dx=aln⁡|x|+bln⁡x7+1+c, then

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$If \int \frac{1 - x^{7}}{x (1 + x^{7})} d x = a \ln | x | + b \ln |x^{7} + 1| + c, then$