What is the integral of (ln(x^{24}))/x ?

The integral of (ln(x^{24}))/x is 12ln^2(x)+C

Popular >

integral of (ln(x^{24}))/x

\int \frac{ln ( x ^{24} )}{x} d x

12 ln^{2} (x) + C

Solution steps

\int \frac{ln ( x ^{24} )}{x} d x

Simplify

ln (x^{24}) : 24 ln (x)

= \int \frac{24 ln ( x )}{x} d x

Take the constant out:

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

= 24 \cdot \int \frac{ln ( x )}{x} d x

Apply u-substitution

: \int u d u

= 24 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 24 \cdot \frac{u ^{2}}{2}

Substitute back

u = ln (x)

= 24 \cdot \frac{ln ^{2} ( x )}{2}

Simplify

24 \cdot \frac{ln ^{2} ( x )}{2} : 12 ln^{2} (x)

= 12 ln^{2} (x)

Add a constant to the solution

= 12 ln^{2} (x) + C

\int \frac{5}{3 x ^{4}} d x

\int \frac{16 x ^{2}}{( x - 18 ) ( x + 6 ) ^{2}} d x

\int \frac{2 x + 1}{x + x ^{2}} d x

\int sin (\frac{π x}{4}) d x

What is the integral of (ln(x^{24}))/x ?
The integral of (ln(x^{24}))/x is 12ln^2(x)+C