What is the integral of (ln(x^{14}))/x ?

The integral of (ln(x^{14}))/x is 7ln^2(x)+C

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integral of (ln(x^{14}))/x

\int \frac{ln ( x ^{14} )}{x} d x

7 ln^{2} (x) + C

Solution steps

\int \frac{ln ( x ^{14} )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{14 u} d u

= \int \frac{ln ( u )}{14 u} d u

Take the constant out:

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

= \frac{1}{14} \cdot \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \frac{1}{14} \cdot \int v d v

Apply the Power Rule

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

= \frac{1}{14} \cdot \frac{v ^{2}}{2}

Substitute back

= \frac{1}{14} \cdot \frac{ln ^{2} ( x ^{14} )}{2}

Simplify

\frac{1}{14} \cdot \frac{ln ^{2} ( x ^{14} )}{2} : 7 ln^{2} (x)

= 7 ln^{2} (x)

Add a constant to the solution

= 7 ln^{2} (x) + C

\frac{\partial}{\partial x} (- y^{3} - x)

\int sin^{3} (\frac{x}{2}) cos (\frac{x}{2}) d x

\frac{e ^{- 3 s}}{s ^{2} + 6 s + 13}

f (x) = 13

\int \frac{1 + u}{- 2 u - 1 - u ^{2}} d u

What is the integral of (ln(x^{14}))/x ?
The integral of (ln(x^{14}))/x is 7ln^2(x)+C