Resources for Integration of Exponential Functions
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Questions
14
With Worked SolutionClick Here -
Video Tutorials
2
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HSC Questions
3
With Worked SolutionClick Here
Integration of Exponential Functions Theory
![\(\displaystyle \int e^{a x+b} d x=\dfrac{1}{a} e^{a x+b}+c\)\\ \begin{multicols}{2} \textbf{Example 1}\\ %24724 Find \(\displaystyle \int {\dfrac{{{e^{ - x}} - 1}}{{{e^{ - x}}}}} \,\,dx\)\\ \textbf{Example 1 solution}\\ $\begin{aligned} \int \frac{e^{-x}-1}{e^{-x}} d x &=\int \frac{e^{-x}}{e^{-x}}-\frac{1}{e^{-x}} d x \\ &=\int 1-e^{x} d x \\ &=x-e^{x}+c \end{aligned}$\\ \columnbreak \textbf{Example 2}\\ %Example 2 (30981) Evaluate \(\displaystyle \displaystyle \int_0^{\ln 2} \, e^{3x} \, dx\)\\ \textbf{Example 2 solution}\\ $\begin{aligned} \int_0^{\ln 2} e^{3x} \, dx &= \left[ \frac{1}{3}e^{3x} \right]_0^{\ln 2}\\&= \frac{1}{3} \left[ e^{3\ln 2} - e^{0} \right]\\&= \frac{1}{3} \left[e^{\ln 8} - 1 \right]\\&= \frac{1}{3} [8-1]\\&= \frac{7}{3} = 2\frac{1}{3} \end{aligned}$\\ \end{multicols}](/media/xieffp0o/4781.png)