What is the integral of ((ln(x^4)))/x ?

The integral of ((ln(x^4)))/x is 2ln^2(x)+C

Popular >

integral of ((ln(x^4)))/x

\int \frac{( ln ( x ^{4} ) )}{x} d x

2 ln^{2} (x) + C

Solution steps

\int \frac{ln ( x ^{4} )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{4 u} d u

= \int \frac{ln ( u )}{4 u} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \frac{1}{4} \cdot \int v d v

Apply the Power Rule

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

= \frac{1}{4} \cdot \frac{v ^{2}}{2}

Substitute back

= \frac{1}{4} \cdot \frac{ln ^{2} ( x ^{4} )}{2}

Simplify

\frac{1}{4} \cdot \frac{ln ^{2} ( x ^{4} )}{2} : 2 ln^{2} (x)

= 2 ln^{2} (x)

Add a constant to the solution

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

\frac{\partial}{\partial x} (2 y^{2} x)

\int e^{\frac{1}{x}} - e^{\frac{1}{x + 1}} d x

\frac{d}{d x} (ln (e^{x} - y))

\int x^{3} x^{2} - 1 d x

\frac{d}{d x} (\frac{1}{( x ^{2} - 1 ) ( x ^{2} + 3 x + 3 )})

What is the integral of ((ln(x^4)))/x ?
The integral of ((ln(x^4)))/x is 2ln^2(x)+C