What is the integral of (ln(x))^5 1/x ?

The integral of (ln(x))^5 1/x is (ln^6(x))/6+C

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integral of (ln(x))^5 1/x

\int (ln (x))^{5} \frac{1}{x} d x

\frac{ln ^{6} ( x )}{6} + C

Solution steps

\int (ln (x))^{5} \frac{1}{x} d x

Simplify

(ln (x))^{5} \frac{1}{x} : \frac{ln ^{5} ( x )}{x}

= \int \frac{ln ^{5} ( x )}{x} d x

Apply u-substitution

: \int u^{5} d u

= \int u^{5} d u

Apply the Power Rule

: \frac{u ^{6}}{6}

= \frac{u ^{6}}{6}

Substitute back

u = ln (x)

= \frac{ln ^{6} ( x )}{6}

Add a constant to the solution

= \frac{ln ^{6} ( x )}{6} + C

\frac{d y}{d x} + x y = x

f (x) = \frac{1}{4 x ^{2} + 3 x}

\int (2 x + 1) e^{- x} d x

x \to 3 lim (x (x - 3))

y^{^{'''}} - 2 y^{^{'}} - 4 y = 0

What is the integral of (ln(x))^5 1/x ?
The integral of (ln(x))^5 1/x is (ln^6(x))/6+C