Question

$\int \frac{1}{x^2{\left(x^4+1\right)}^{3/4}}dx$ is equal to

• A. $\frac{-{\left(1+x^4\right)}^{1/4}}{x}+C$
• B. $\frac{-{\left(1+x^4\right)}^{1/4}}{x^2}+C$
• C. $\frac{-{\left(1+x^4\right)}^{1/4}}{2x}+C$
• D. $\frac{-{\left(1+x^4\right)}^{3/4}}{x}+C$

Answer 1

Answer: (A)

$\int \frac{\left(1/x^5\right)dx}{{\left(1+\frac{1}{x^4}\right)}^{3/4}}$
$=-{\left(1+\frac{1}{x^4}\right)}^{1/4}=\frac{{\left(x^4+1\right)}^{1/4}}{x}$