What is the integral of (ln(x^{10}))/x ?

The integral of (ln(x^{10}))/x is 5ln^2(x)+C

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integral of (ln(x^{10}))/x

\int \frac{ln ( x ^{10} )}{x} d x

5 ln^{2} (x) + C

Solution steps

\int \frac{ln ( x ^{10} )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{10 u} d u

= \int \frac{ln ( u )}{10 u} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{10} \cdot \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \frac{1}{10} \cdot \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{1}{10} \cdot \frac{v ^{2}}{2}

Substitute back

= \frac{1}{10} \cdot \frac{ln ^{2} ( x ^{10} )}{2}

Simplify

\frac{1}{10} \cdot \frac{ln ^{2} ( x ^{10} )}{2} : 5 ln^{2} (x)

= 5 ln^{2} (x)

Add a constant to the solution

= 5 ln^{2} (x) + C

\frac{2 s - 6}{s ^{2} - 9}

x \to 0 lim (\frac{( sin ( 8 x ) )}{3 x})

\frac{d}{d x} (cos (3 x + 3))

x \to - 2 + lim (\frac{2 x + 1}{2 + x})

cos (x^{2}) \cdot 2 x

What is the integral of (ln(x^{10}))/x ?
The integral of (ln(x^{10}))/x is 5ln^2(x)+C