Evaluate using partial integration formula of \int _{ }^{ }\ln \left(x\right)

x\ln{\left(x\right)}-x+C,C \in \mathbb{R}

Solve int _ ^ ln (x) - Socratic AI (ScanMath)

Evaluate

\int ln (x) d x

Prepare for integration by parts

u = ln (x) d v = d x

Calculate the derivative

More Steps

d u = \frac{1}{x} d x d v = d x

Evaluate the integral

More Steps

d u = \frac{1}{x} d x v = x

Substitute u = ln (x) 、 v = x 、 d u = \frac{1}{x} d x 、 d v = d x for \int u d v = uv - \int v d u

ln (x) \times x - \int \frac{1}{x} \times x d x

Calculate

x ln (x) - \int 1 d x

Use the property of integral \int k d x = k x

x ln (x) - x

Solution

x ln (x) - x + C, C \in R