Question

question 2 (1 point)
the substitution ( u = 3x ) transforms the integral ( int e^{3x}dx ) into
( \bigcirc int \frac{1}{9}e^{u}du )
( \bigcirc int \frac{1}{3}e^{u}du )
( \bigcirc int e^{3u}du )
( \bigcirc int \frac{1}{3}e^{3u}du )
( \bigcirc int e^{u}du )

Explanation:

Step1: Differentiate \(u = 3x\)

If \(u = 3x\), then \(du=3dx\), and \(dx=\frac{1}{3}du\).

Step2: Substitute \(u\) and \(dx\) into the integral

The original integral \(\int e^{3x}dx\) becomes \(\int e^{u}\cdot\frac{1}{3}du=\int\frac{1}{3}e^{u}du\)

Answer:

\(\int\frac{1}{3}e^{u}du\) (the second option)