Evaluate integral of 1/(x natural log of x^4) with respect to x

$\int \frac{1}{x \ln (x^{4})} d x$

Rewrite as $\int \frac{1}{x (4 \ln (x))} d x$ .

$\int \frac{1}{x (4 \ln (x))} d x$

Since $\frac{1}{4}$ is constant with respect to $x$ , move $\frac{1}{4}$ out of the integral.

$\frac{1}{4} \int \frac{1}{x (\ln (x))} d x$

Let $u = \ln (x)$ . Then $d u = \frac{1}{x} d x$ , so $x d u = d x$ . Rewrite using $u$ and $d$ $u$ .

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Let $u = \ln (x)$ . Find $\frac{d u}{d x}$ .

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Differentiate $\ln (x)$ .

$\frac{d}{d x} [\ln (x)]$

The derivative of $\ln (x)$ with respect to $x$ is $\frac{1}{x}$ .

$\frac{1}{x}$

Rewrite the problem using $u$ and $d u$ .

$\frac{1}{4} \int \frac{1}{u} d u$

The integral of $\frac{1}{u}$ with respect to $u$ is $\ln (| u |)$ .

$\frac{1}{4} (\ln (| u |) + C)$

Simplify.

$\frac{1}{4} \ln (| u |) + C$

Replace all occurrences of $u$ with $\ln (x)$ .

$\frac{1}{4} \ln (| \ln (x) |) + C$

Evaluate integral of 1/(x natural log of x^4) with respect to x

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