Calculus Examples

$\frac{4 + u}{u}$

Step 1

Split the fraction into multiple fractions.

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

Step 2

Split the single integral into multiple integrals.

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

Step 3

Cancel the common factor of $u$ .

Tap for more steps...

Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

Since $4$ is constant with respect to $u$ , move $4$ out of the integral.

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

Step 5

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

$4 (\ln (| u |) + C) + \int d u$

Step 6

Apply the constant rule.

$4 (\ln (| u |) + C) + u + C$

Step 7

Simplify.

$4 \ln (| u |) + u + C$