Calculus Examples

$\int \frac{2}{2 x - 3} d x$

Step 1

Let $u = 2 x - 3$ . Then $d u = 2 d x$ , so $\frac{1}{2} d u = d x$ . Rewrite using $u$ and $d$ $u$ .

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Step 1.1

Let $u = 2 x - 3$ . Find $\frac{d u}{d x}$ .

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Step 1.1.1

Rewrite.

$\frac{2}{1}$

Step 1.1.2

Divide $2$ by $1$ .

$2$

Step 1.2

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

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

Step 2

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

$\ln (| u |) + C$

Step 3

Replace all occurrences of $u$ with $2 x - 3$ .

$\ln (| 2 x - 3 |) + C$