What is the integral of ((ln(x))^{28})/x ?

The integral of ((ln(x))^{28})/x is (ln^{29}(x))/(29)+C

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integral of ((ln(x))^{28})/x

\int \frac{( ln ( x ) ) ^{28}}{x} d x

\frac{ln ^{29} ( x )}{29} + C

Solution steps

\int \frac{( ln ( x ) ) ^{28}}{x} d x

Apply u-substitution

: \int u^{28} d u

= \int u^{28} d u

Apply the Power Rule

: \frac{u ^{29}}{29}

= \frac{u ^{29}}{29}

Substitute back

u = ln (x)

= \frac{ln ^{29} ( x )}{29}

Add a constant to the solution

= \frac{ln ^{29} ( x )}{29} + C

\frac{d}{d x} (arcsin (3 x + 1))

\frac{\partial}{\partial z} (x y z^{2} tan (y t))

sin^{2} (x)

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

\frac{d}{d t} (- 1)

What is the integral of ((ln(x))^{28})/x ?
The integral of ((ln(x))^{28})/x is (ln^{29}(x))/(29)+C