What is the integral of (ln(x^{20}))/x ?

The integral of (ln(x^{20}))/x is 10ln^2(x)+C

Popular >

integral of (ln(x^{20}))/x

\int \frac{ln ( x ^{20} )}{x} d x

10 ln^{2} (x) + C

Solution steps

\int \frac{ln ( x ^{20} )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{20 u} d u

= \int \frac{ln ( u )}{20 u} d u

Take the constant out:

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

= \frac{1}{20} \cdot \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \frac{1}{20} \cdot \int v d v

Apply the Power Rule

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

= \frac{1}{20} \cdot \frac{v ^{2}}{2}

Substitute back

= \frac{1}{20} \cdot \frac{ln ^{2} ( x ^{20} )}{2}

Simplify

\frac{1}{20} \cdot \frac{ln ^{2} ( x ^{20} )}{2} : 10 ln^{2} (x)

= 10 ln^{2} (x)

Add a constant to the solution

= 10 ln^{2} (x) + C

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

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

\frac{d}{d x} (cos (2 x) sin (x))

\int t^{5} - 7 t d t

\frac{\partial}{\partial x} (2 x^{2} + 4 y^{2} + 1)

What is the integral of (ln(x^{20}))/x ?
The integral of (ln(x^{20}))/x is 10ln^2(x)+C