What is the integral of ((ln(x))^{50})/x ?

The integral of ((ln(x))^{50})/x is (ln^{51}(x))/(51)+C

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integral of ((ln(x))^{50})/x

\int \frac{( ln ( x ) ) ^{50}}{x} d x

\frac{ln ^{51} ( x )}{51} + C

Solution steps

\int \frac{( ln ( x ) ) ^{50}}{x} d x

Apply u-substitution

: \int u^{50} d u

= \int u^{50} d u

Apply the Power Rule

: \frac{u ^{51}}{51}

= \frac{u ^{51}}{51}

Substitute back

u = ln (x)

= \frac{ln ^{51} ( x )}{51}

Add a constant to the solution

= \frac{ln ^{51} ( x )}{51} + C

s^{2}

(\frac{x}{x ^{2} + 1})^{^{'}}

\int cos (x) sin (x) e^{- 2 c o s (x)} d x

y^{^{'}} = 2 x (x - 4)

x \to π + lim (csc (x))

What is the integral of ((ln(x))^{50})/x ?
The integral of ((ln(x))^{50})/x is (ln^{51}(x))/(51)+C