x-4-x-1-4-x-5-dx-

Question Number 53357 by gunawan last updated on 20/Jan/19

\int \frac{{(x^{4} - x)}^{1 / 4}}{x^{5}} d x =

Answered by tanmay.chaudhury50@gmail.com last updated on 21/Jan/19

\int \frac{{x^{4} (1 - \frac{1}{x^{3}})}^{\frac{1}{4}}}{x^{5}} d x

\int \frac{{(1 - \frac{1}{x^{3}})}^{\frac{1}{4}}}{x^{4}} d x

t^{4} = 1 - \frac{1}{x^{3}}

4 t^{3} d t = (0 + \frac{3}{x^{4}}) d x

\frac{4 t^{3}}{3} d t = \frac{d x}{x^{4}}

\int \frac{{(t^{4})}^{\frac{1}{4}} \times \frac{4 t^{3}}{3} d t}{1} \times

\frac{4}{3} \int t^{4} d t

\frac{4}{15} \times t^{5} + c

\frac{4}{15} \times {(1 - \frac{1}{x^{3}})}^{\frac{5}{4}} + c