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JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int {\frac{{dx}}{{x + {x^7}}}} = p(x)\) then, \(\int {\frac{{{x^6}}}{{x + {x^7}}}} dx\) is equal to
- A \(\ln \,\left| x \right| - p\left( x \right) + c\)
- B \(\ln \,\left| x \right| + p\left( x \right) + c\)
- C \(x - p\left( x \right) + c\)
- D \(x + p\left( x \right) + c\)
Answer & Solution
Correct Answer
(A) \(\ln \,\left| x \right| - p\left( x \right) + c\)
Step-by-step Solution
Detailed explanation
\(\int \frac{x^{6}}{x+x^{7}} d x=\int \frac{x^{6}}{x\left(1+x^{6}\right)} d x\) \(\int {\frac{{\left( {1 + {x^6}} \right) - 1}}{{x\left( {1 + {x^6}} \right)}}} dx\) \(=\int \frac{1}{x} d x-\int \frac{1}{x+x^{7}} d x\) \(=\ln |x|-p(x)+c\)
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