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If $\int \frac{d x}{x+x^7}=p(x)$ then, $\int \frac{x^6}{x+x^7} d x$ is equal to:
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Verified Answer
The correct answer is:
$\ln |x|-p(x)+c$
$\ln |x|-p(x)+c$
$\int \frac{x^6}{x+x^7} d x=\int \frac{x^6}{x\left(1+x^6\right)} d x$
$=\int \frac{\left(1+x^6\right)-1}{x\left(1+x^6\right)} d x$
$=\int \frac{1}{x} d x-\int \frac{1}{x+x^7} d x$
$=\ln |x|-p(x)+c$
$=\int \frac{\left(1+x^6\right)-1}{x\left(1+x^6\right)} d x$
$=\int \frac{1}{x} d x-\int \frac{1}{x+x^7} d x$
$=\ln |x|-p(x)+c$
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