Mathematics

# Solve: $\displaystyle \int \dfrac{(x^4 - x)^{1/4}}{x^5}dx.$

##### SOLUTION
Now,
$\displaystyle \int \dfrac{(x^4 - x)^{1/4}}{x^5}dx$
$=\displaystyle \int \dfrac{(1 - \dfrac{1}{x^3})^{1/4}}{x^4}dx$
Let, $1-\dfrac{1}{x^3}=z$ then $\dfrac{3}{x^4}dx=dz$
Using these in the above expression we get,
$=\displaystyle \int \dfrac{{z^{1/4}}}{3}dz$
$=\dfrac{4}{15}z^{5/4}+c$ [ Where $c$ is integrating constant]
$=\dfrac{4}{15}(1-\dfrac{1}{x^3})^{5/4}+c$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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