Calculus Examples

$\int \frac{2 x^{13}}{x^{14}} d x$

Step 1

Cancel the common factor of $x^{13}$ and $x^{14}$ .

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Step 1.1

Factor $x^{13}$ out of $2 x^{13}$ .

$\int \frac{x^{13} \cdot 2}{x^{14}} d x$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $x^{13}$ out of $x^{14}$ .

$\int \frac{x^{13} \cdot 2}{x^{13} x} d x$

Step 1.2.2

Cancel the common factor.

$\int \frac{x^{13} \cdot 2}{x^{13} x} d x$

Step 1.2.3

Rewrite the expression.

$\int \frac{2}{x} d x$

Step 2

Since $2$ is constant with respect to $x$ , move $2$ out of the integral.

$2 \int \frac{1}{x} d x$

Step 3

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

$2 (\ln (| x |) + C)$

Step 4

Simplify.

$2 \ln (| x |) + C$