Question

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

Answer 1

Answer: (A)

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