Calculus Examples

$\frac{1}{p} d P$

Step 1

Simplify.

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Step 1.1

Combine $d$ and $\frac{1}{p}$ .

$\int \frac{d}{p} \cdot P d p$

Step 1.2

Combine $\frac{d}{p}$ and $P$ .

$\int \frac{d P}{p} d p$

Step 2

Since $d P$ is constant with respect to $p$ , move $d P$ out of the integral.

$d P \int \frac{1}{p} d p$

Step 3

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

$d P (\ln (| p |) + C)$

Step 4

Simplify.

$d P \ln (| p |) + C$