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

\frac{d}{d x} (e^{(x + y)} - 1)

f (x) = (1 + 5 x)^{9}, (0, 1)

e^{- x}, 1

\frac{\partial}{\partial x} ((cos (x))^{2})

- \frac{1}{( x - 6 ) ^{2}}

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