Integrate the following exponential expressions with respect to $x$: \(\displaystyle\displaystyle

Question

Integrate the following exponential expressions with respect to $x$: $\displaystyle\displaystyle \displaystyle\int \mathrm{e}^{3x+2} \, \mathrm{d}x$ $\displaystyle\displaystyle \displaystyle\int \frac{\mathrm{e}^{5x}+2}{\mathrm{e}^{5x}} \, \mathrm{d}x$ $\displaystyle\displaystyle \displaystyle\int \frac{(\mathrm{e}^{3x}-\mathrm{e}^{x})^2}{\mathrm{e}^{x}} \, \mathrm{d}x$ $\displaystyle\displaystyle \displaystyle\int \frac{2-\mathrm{e}^{3-2x}}{\mathrm{e}^{3-2x}} \, \mathrm{d}x$

Accepted Answer

(a) $\dfrac13\mathrm e^{3x+2}+C$ (b) $x-\dfrac25\mathrm e^{-5x}+C$ (c) $\dfrac15\mathrm e^{5x}-\dfrac23\mathrm e^{3x}+\mathrm e^x+C$ (d) $\mathrm e^{2x-3}-x+C$

Integration - Integration of Exponential Functions

Integration - Integration of Exponential Functions

Solution:

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