Mathematics

# If $\int \dfrac{dx}{x+x^{7}}=p(x)$ then , $\int \dfrac{x^{6}}{x+x^{7}}dx$ is eqaul to:

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

##### SOLUTION
$\int{\cfrac{dx}{x + {x}^{7}}} = p\left( x \right) \quad \left( \text{Given} \right)$

Now,
$\int{\cfrac{{x}^{6}}{x + {x}^{7}} dx} \\ = \int{\cfrac{{x}^{6} + 1 - 1}{x + {x}^{7}} dx} \\ = \int{\cfrac{{x}^{6} + 1}{x + {x}^{7}} dx} - \int{\cfrac{dx}{x + {x}^{7}}} \\ = \int{\cfrac{{x}^{6} + 1}{x \left( 1 + {x}^{6} \right)} dx} - \int{\cfrac{dx}{x + {x}^{7}} dx} \\ = \ln{\left| x \right|} - p \left( x \right) + c$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 One Word Medium
The value of $\displaystyle \int_{0}^{1/2}\frac{dx}{\sqrt{\left ( x-x^{2} \right )}}$is $\displaystyle \frac{\pi }{k}.$ Find the value of $k$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Hard
Evaluate the following integrals:$\displaystyle \int \sqrt{3x^{2}+4}dx$
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• C. None of these
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1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
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Q4 Subjective Hard
Prove that:
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