Question

$\int \frac{(x-x^5{)}^{1/5}}{x^6}dx$ is equal to

• A. $\frac{5}{24}{(\frac{1}{x^4}-1)}^{6/5}+C$
• B. $\frac{5}{24}{(1-\frac{1}{x^4})}^{6/5}+C$
• C. $-\frac{5}{24}{(\frac{1}{x^4}-1)}^{6/5}+C$
• D. None of these

Answer 1

The correct option is C $-\frac{5}{24}{(\frac{1}{x^4}-1)}^{6/5}+C$

$\int \frac{(x-x^5{)}^{1/5}}{x^6}dx=\int \frac{{(\frac{1}{x^4}-1)}^{1/5}}{x^5}dx=-\frac{1}{4}\int t^{1/5}dt=[Putting\frac{1}{x^4}-1=t\Rightarrow \frac{dx}{x^5}=-\frac{1}{4}dt]=-\frac{5}{24}{t}^{\frac{6}{5}}+C=-\frac{5}{24}{(\frac{1}{x^4}-1)}^{\frac{6}{5}}+C$