What is the integral of ((ln(x))^{48})/x ?

The integral of ((ln(x))^{48})/x is (ln^{49}(x))/(49)+C

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integral of ((ln(x))^{48})/x

\int \frac{( ln ( x ) ) ^{48}}{x} d x

\frac{ln ^{49} ( x )}{49} + C

Solution steps

\int \frac{( ln ( x ) ) ^{48}}{x} d x

Apply u-substitution

: \int u^{48} d u

= \int u^{48} d u

Apply the Power Rule

: \frac{u ^{49}}{49}

= \frac{u ^{49}}{49}

Substitute back

u = ln (x)

= \frac{ln ^{49} ( x )}{49}

Add a constant to the solution

= \frac{ln ^{49} ( x )}{49} + C

ln (3 - 5 x)

\frac{d}{d x} (\frac{3 tan ( x )}{x})

f (x) = \frac{( a x + b )}{c x + d}

\frac{1}{8} y^{3}

\frac{d ^{2}}{d x ^{2}} (5 csc (x))

What is the integral of ((ln(x))^{48})/x ?
The integral of ((ln(x))^{48})/x is (ln^{49}(x))/(49)+C