What is the integral of ((ln(x^{34})))/x ?

The integral of ((ln(x^{34})))/x is 17ln^2(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((ln(x^{34})))/x

\int \frac{( ln ( x ^{34} ) )}{x} d x

17 ln^{2} (x) + C

Solution steps

\int \frac{ln ( x ^{34} )}{x} d x

Apply u-substitution

: \int \frac{ln ( u )}{34 u} d u

= \int \frac{ln ( u )}{34 u} d u

Take the constant out:

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

= \frac{1}{34} \cdot \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \frac{1}{34} \cdot \int v d v

Apply the Power Rule

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

= \frac{1}{34} \cdot \frac{v ^{2}}{2}

Substitute back

= \frac{1}{34} \cdot \frac{ln ^{2} ( x ^{34} )}{2}

Simplify

\frac{1}{34} \cdot \frac{ln ^{2} ( x ^{34} )}{2} : 17 ln^{2} (x)

= 17 ln^{2} (x)

Add a constant to the solution

= 17 ln^{2} (x) + C

cos (x) sin^{2} (x)

\int e^{2 x} (x - 1) d x

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

\int \frac{1}{( 1 - 4 x ) ^{3}} d x

\int 1 + (6 x)^{2} d x

What is the integral of ((ln(x^{34})))/x ?
The integral of ((ln(x^{34})))/x is 17ln^2(x)+C