What is the integral of 1/(xln(x^7)) ?

The integral of 1/(xln(x^7)) is 1/7 ln(7|ln(x)|)+C

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integral of 1/(xln(x^7))

\int \frac{1}{x ln ( x ^{7} )} d x

\frac{1}{7} ln (7 ∣ ln (x) ∣) + C

Solution steps

\int \frac{1}{x ln ( x ^{7} )} d x

Apply u-substitution

: \int \frac{1}{7 u ln ( u )} d u

= \int \frac{1}{7 u ln ( u )} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int \frac{1}{u ln ( u )} d u

Apply u-substitution

: \int \frac{1}{v} d v

= \frac{1}{7} \cdot \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= \frac{1}{7} ln ∣ v ∣

Substitute back

= \frac{1}{7} ln ln (x^{7})

Simplify

\frac{1}{7} ln ln (x^{7}) : \frac{1}{7} ln (7 ∣ ln (x) ∣)

= \frac{1}{7} ln (7 ∣ ln (x) ∣)

Add a constant to the solution

= \frac{1}{7} ln (7 ∣ ln (x) ∣) + C

\int e^{2 θ} d θ

\int e^{2 x} tan^{2} (e^{2 x}) d x

\frac{d}{d x} (2 a cos (2 x) - 2 b sin (2 x))

r \frac{2 x}{3 x ^{2} - 4}

f (x) = \frac{x ^{2} - 2 x}{x}

What is the integral of 1/(xln(x^7)) ?
The integral of 1/(xln(x^7)) is 1/7 ln(7|ln(x)|)+C