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
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