Find the indefinite integral. $\int \frac { ( \ln x ) ^ { 4 } } { x } d x$
A) $\frac { ( \ln x ) ^ { 4 } } { 4 } + C$
B) $4 ( \ln x ) ^ { 3 } + C$
C) $\frac { 5 \ln x } { x } + C$
D) $\frac { ( \ln x ) ^ { 5 } } { 5 } + C$
E)none of the above

Question

Quizplus · Accepted Answer

The integral $\int \frac { ( \ln x ) ^ { 4 } } { x } d x$ can be solved by recognizing it as a standard form where the integral of $\frac{(\ln x)^n}{x} dx$ is $\frac{(\ln x)^{n+1}}{n+1} + C$. Applying this, we get $\frac { ( \ln x ) ^ { 5 } } { 5 } + C$.

Find the Indefinite Integral ∫(ln⁡x)4xdx\int \frac { ( \ln x ) ^ { 4 } } { x } d x∫x(lnx)4​dx

Find the Indefinite Integral $\int \frac { ( \ln x ) ^ { 4 } } { x } d x$