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Q.

If $\int \frac{d x}{x + x^{7}} = p (x),$ then $\int \frac{x^{6}}{x + x^{7}} d x =$

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a

$\log |x| - p (x) + c$

b

$\log |x| + p (x) + c$

c

$x - p (x) + c$

d

$x + p (x) + c$

answer is A.

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Detailed Solution

$\int \frac{x^{7}}{x (x + x^{7})} d x = \int \frac{(x + x^{7}) - x}{x (x + x^{7})} d x = \int (\frac{1}{x} - \frac{1}{x + x^{7}}) d x$

$= \log |x| - p (x) + c$

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If ∫dxx+x7=p(x), then ∫x6x+x7dx=