Evaluate the integral.
-$$\int _ { 1 } ^ { 3 } \ln 5 x d x$$
A) 8.51
B) -3.49
C) 14.4
D) 4.51

Question

Quizplus · Accepted Answer

The integral of $\ln(5x)$ can be found using integration by parts. Let $u = \ln(5x)$ and $dv = dx$. Then $du = \frac{1}{x} dx$ and $v = x$. The integral becomes $x \ln(5x) - \int x \cdot \frac{1}{x} dx = x \ln(5x) - \int dx = x \ln(5x) - x$. Evaluate from 1 to 3: $[3 \ln(15) - 3] - [1 \ln(5) - 1]$, which simplifies to approximately 4.51.

Evaluate the Integral ∫13ln⁡5xdx\int _ { 1 } ^ { 3 } \ln 5 x d x∫13​ln5xdx

Evaluate the Integral $\int _ { 1 } ^ { 3 } \ln 5 x d x$