Question

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

• A. $\ln x+\frac{2}{7}\ln (1+x^7)+c$
• B. $\ln x-\frac{2}{7}\ln (1-x^7)+c$
• C. $\ln x-\frac{2}{7}\ln (1+x^7)+c$
• D. $\ln x+\frac{2}{7}\ln (1-x^7)+c$

Answer 1

The correct option is C $\ln x-\frac{2}{7}\ln (1+x^7)+c$

Given , $\int \frac{1-x^7}{x(1+x^7)}dx$
$\Rightarrow$ $\int \frac{1+x^7-2x^7}{x(1+x^7)}dx$
$\Rightarrow$ $\int (\frac{1}{x}-\frac{2x^6}{1+x^7})dx$
$\Rightarrow$ $\int (\frac{1}{x}-\frac{2}{7}(\frac{7x^6}{1+x^7}\left)\right)dx$
$\Rightarrow$ $\ln x-\frac{2}{7}\ln (1+x^7)+c$
Hence, option 'C' is correct.