Calculus Examples

$\int \ln (u) d u$

Step 1

Integrate by parts using the formula $\int w d v = w v - \int v d w$ , where $w = \ln (u)$ and $dv = 1$ .

$\ln (u) u - \int u \frac{1}{u} d u$

Step 2

Simplify.

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Combine $u$ and $\frac{1}{u}$ .

$\ln (u) u - \int \frac{u}{u} d u$

Cancel the common factor of $u$ .

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Cancel the common factor.

$\ln (u) u - \int \frac{u}{u} d u$

Rewrite the expression.

$\ln (u) u - \int d u$

Step 3

Apply the constant rule.

$\ln (u) u - (u + C)$

Step 4

Simplify.

$\ln (u) u - u + C$