What is the integral of (ln^6(x))/x ?

The integral of (ln^6(x))/x is (ln^7(x))/7+C

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integral of (ln^6(x))/x

\int \frac{ln ^{6} ( x )}{x} d x

\frac{ln ^{7} ( x )}{7} + C

Solution steps

\int \frac{ln ^{6} ( x )}{x} d x

Apply u-substitution

: \int u^{6} d u

= \int u^{6} d u

Apply the Power Rule

: \frac{u ^{7}}{7}

= \frac{u ^{7}}{7}

Substitute back

u = ln (x)

= \frac{ln ^{7} ( x )}{7}

Add a constant to the solution

= \frac{ln ^{7} ( x )}{7} + C

x \to 0 lim (\frac{3 sin ( x ) + x}{x})

\int \frac{1}{3 x ( 5 + x )} d x

y = x^{4} + 7 e^{x}, (0, 7)

x \to 2 - lim (H (x))

\frac{d}{d x} (x (2 x + 9)^{\frac{1}{3}})

What is the integral of (ln^6(x))/x ?
The integral of (ln^6(x))/x is (ln^7(x))/7+C