Question

1. ∫12e4xdx

Explanation:

Step1: Rewrite the integrand

We know that \(\frac{1}{e^{4x}} = e^{-4x}\), so the integral becomes \(\int 12e^{-4x}dx\).

Step2: Use the integral formula \(\int ae^{bx}dx=\frac{a}{b}e^{bx}+C\) (\(a = 12\), \(b=-4\))

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Answer:

\(-3e^{-4x}+C\)