Mathematics

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

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

##### 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
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Solve $\int {{{\left( {2x + 3} \right)}^2}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int\frac{xTan^{-1}x}{(1+x^{2})^{3/_{2}}}dx=$
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