Mathematics

$$\displaystyle \int \frac{1-x^7}{x(1+x^7)} dx$$ equals


ANSWER

$$\ln x-\displaystyle \frac{2}{7}\ln(1+x^7)+c$$


SOLUTION
Given , $$\displaystyle \int \frac{1-x^7}{x(1+x^7)} dx$$

$$\Rightarrow$$ $$\displaystyle \int \frac{1+x^7-2x^7}{x(1+x^7)} dx$$

$$\Rightarrow$$ $$\displaystyle \int( \frac{1}{x}-\frac{2x^6}{1+x^7}) dx$$

$$\Rightarrow$$ $$\displaystyle \int( \frac{1}{x}-\frac{2}{7}(\frac{7x^6}{1+x^7})) dx$$

$$\Rightarrow$$ $$ \ln {x} -\dfrac{2}{7} \ln {(1+x^7)} +c $$
Hence, option 'C' is correct.
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Single Correct Medium Published on 17th 09, 2020
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