Calculus Examples

$\frac{d u}{u}$

Step 1

Write $\frac{d u}{u}$ as a function.

$f (d) = \frac{d u}{u}$

Step 2

The function $F (d)$ can be found by finding the indefinite integral of the derivative $f (d)$ .

$F (d) = \int f (d) d \cdot d$

Step 3

Set up the integral to solve.

$F (d) = \int \frac{d u}{u} d \cdot d$

Step 4

Split the fraction into multiple fractions.

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Step 4.1

Cancel the common factor.

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

Step 4.2

Divide $d$ by $1$ .

$\int d d \cdot d$

Step 5

By the Power Rule, the integral of $d$ with respect to $d$ is $\frac{1}{2} d^{2}$ .

$\frac{1}{2} d^{2} + C$

Step 6

The answer is the antiderivative of the function $f (d) = \frac{d u}{u}$ .

$F (d) =$ $\frac{1}{2} d^{2} + C$