Integrate $\int \frac{\sqrt[4]{\ln x}}{x} d x$ .
A) $(\ln x)^{5 / 4}+C$
B) $\frac{4}{5}(\ln x)^{5 / 4}+C$
C) $\frac{2(\ln x)^{5 / 4}}{x^{2}}+C$
D) $\frac{\sqrt[5]{\ln x}}{5}+C$

Question

Quizplus · Accepted Answer

To solve the integral $\int \frac{\sqrt[4]{\ln x}}{x} dx$, let $u = \ln x$, which implies $du = \frac{1}{x}dx$. Substituting these into the integral gives $\int u^{1/4} du$, which integrates to $\frac{4}{5}u^{5/4} + C$. Substituting back $u = \ln x$ gives the result $\frac{4}{5}(\ln x)^{5 / 4} + C$.

Integrate ∫ln⁡x4xdx\int \frac{\sqrt[4]{\ln x}}{x} d x∫x4lnx​​dx A) (ln⁡x)5/4+C(\ln x)^{5 / 4}+C(lnx)5/4+C

Integrate $\int \frac{\sqrt[4]{\ln x}}{x} d x$
A) $(\ln x)^{5 / 4}+C$