What is the integral of (60ln(3^{3^{x+1}}))/(3^x-1) ?

The integral of (60ln(3^{3^{x+1}}))/(3^x-1) is 180ln|3^x-1|+C

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integral of (60ln(3^{3^{x+1}}))/(3^x-1)

\int \frac{60 ln ( 3 ^{3^{x + 1}} )}{3 ^{x} - 1} d x

180 ln ∣ 3^{x} - 1 ∣ + C

Solution steps

\int \frac{60 ln ( 3 ^{3^{x + 1}} )}{3 ^{x} - 1} d x

Take the constant out:

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

= 60 \cdot \int \frac{ln ( 3 ^{3^{x + 1}} )}{3 ^{x} - 1} d x

Apply u-substitution

: \int \frac{3}{u} d u

= 60 \cdot \int \frac{3}{u} d u

Take the constant out:

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

= 60 \cdot 3 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 60 \cdot 3 ln ∣ u ∣

Substitute back

u = 3^{x} - 1

= 60 \cdot 3 ln ∣ 3^{x} - 1 ∣

Simplify

= 180 ln ∣ 3^{x} - 1 ∣

Add a constant to the solution

= 180 ln ∣ 3^{x} - 1 ∣ + C

\int x - x^{4} d x

n = 0 \sum \infty 2^{- 2 n}

x \to 0 lim (4^{2})

\frac{d}{d x} (\frac{36}{x})

What is the integral of (60ln(3^{3^{x+1}}))/(3^x-1) ?
The integral of (60ln(3^{3^{x+1}}))/(3^x-1) is 180ln|3^x-1|+C