Integrate the following expressions with respect to $x$. \(\displaystyle\int \mathrm{e}^{1+4x} \,

Question

Integrate the following expressions with respect to $x$.

$\displaystyle\int \mathrm{e}^{1+4x} \, \mathrm{d}x$
$\displaystyle\int (\mathrm{e}^{2-x}-1)^2 \, \mathrm{d}x$
$\displaystyle\int \frac{(2\mathrm{e}^{-x}+\mathrm{e}^x)^2}{\mathrm{e}^x} \, \mathrm{d}x$
$\displaystyle\int \frac{(\mathrm{e}^{\pi x- 1}-\mathrm{e}^x)^2}{\mathrm{e}^{2x}} \, \mathrm{d}x$

Accepted Answer

(a) $\dfrac14e^{1+4x}+C$ (b) $-\dfrac12e^{4-2x}+2e^{2-x}+x+C$ (c) $-\dfrac43e^{-3x}-4e^{-x}+e^x+C$ (d) $\dfrac{e^{(2\pi-2)x-2}}{2\pi-2}-\dfrac{2e^{(\pi-1)x-1}}{\pi-1}+x+C$

Integration - Integration of Exponential Functions

Integration - Integration of Exponential Functions

Solution:

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