Consider the indefinite integral $\int e^{3 x+5} d x$ :
a) This can be transformed into a basic integral by letting
\[
u=
\]
and
\[
d u=
\]

Step 1 ：Let's consider the indefinite integral \(\int e^{3 x+5} d x\)

Step 2 ：We can simplify this integral by using the substitution method. Let's let \(u = 3x + 5\)

Step 3 ：The differential \(du\) would be the derivative of \(u\) with respect to \(x\), which is \(3 dx\)

Step 4 ：In our integral, we have \(dx\), not \(3dx\). To correct for this, we can divide both sides of the equation \(du = 3 dx\) by \(3\) to get \(du/3 = dx\)

Step 5 ：We can then substitute \(u\) and \(du/3\) into the integral

Step 6 ：The integral of \(e^{3x+5}\) with respect to \(x\) is \(\frac{1}{3}e^{3x+5} + C\), where \(C\) is the constant of integration

Step 7 ：Final Answer: \(\boxed{\frac{1}{3}e^{3x+5} + C}\)