What is the integral of ((ln^4(x)))/x ?

The integral of ((ln^4(x)))/x is (ln^5(x))/5+C

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integral of ((ln^4(x)))/x

\int \frac{( ln ^{4} ( x ) )}{x} d x

\frac{ln ^{5} ( x )}{5} + C

Solution steps

\int \frac{ln ^{4} ( x )}{x} d x

Apply u-substitution

: \int u^{4} d u

= \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= \frac{u ^{5}}{5}

Substitute back

u = ln (x)

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

Add a constant to the solution

= \frac{ln ^{5} ( x )}{5} + C

\int \frac{ln ( x + 1 )}{x} d x

\int \frac{3 x}{( 1 + 9 x ^{2} ) ^{4}} d x

sin^{2} (t)

What is the integral of ((ln^4(x)))/x ?
The integral of ((ln^4(x)))/x is (ln^5(x))/5+C