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

Question

Integrate the following expressions with respect to $x$: $\displaystyle\displaystyle \displaystyle\int 4\mathrm{e}^{1-2x} \, \mathrm{d}x$ $\displaystyle\displaystyle \displaystyle\int (\mathrm{e}^{2x}-\mathrm{e}^{-x})^2 \, \mathrm{d}x$ $\displaystyle\displaystyle \displaystyle\int \frac{(\mathrm{e}^{3x}+\mathrm{e}^{-x})^2}{\mathrm{e}^{2x}} \, \mathrm{d}x$ $\displaystyle\displaystyle \displaystyle\int \frac{5-\mathrm{e}^{1-4x}}{\mathrm{e}^{1-4x}} \, \mathrm{d}x$

Accepted Answer

(a) $-2\mathrm e^{1-2x}+C$ (b) $\dfrac14\mathrm e^{4x}-2\mathrm e^x-\dfrac12\mathrm e^{-2x}+C$ (c) $\dfrac14\mathrm e^{4x}+2x-\dfrac14\mathrm e^{-4x}+C$ (d) $\dfrac54\mathrm e^{4x-1}-x+C$

Integration - Integration of Exponential Functions

Integration - Integration of Exponential Functions

Solution:

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