\(\int \mathrm e^x\,\mathrm dx=\mathrm e^x+C\qquad\int \mathrm e^{ax+b}\,\mathrm dx=\dfrac{\mathrm e

Question

$\int \mathrm e^x\,\mathrm dx=\mathrm e^x+C\qquad\int \mathrm e^{ax+b}\,\mathrm dx=\dfrac{\mathrm e^{ax+b}}a+C\quad(a\ne0)$ Divide by the coefficient of $x$ in the exponent. If $a = 0$, the integrand is constant. Check by differentiating. Example Integrate $\mathrm e^{2x-1}$ with respect to $x$. $\int\mathrm{e}^{2x-1}\,\mathrm{d}x$${}=\dfrac{\mathrm{e}^{2x-1}}{2}+C$ Integrate $\mathrm e^{3-x}$ with respect to $x$. $\int\mathrm{e}^{3-x}\,\mathrm{d}x$${}=\dfrac{\mathrm{e}^{3-x}}{-1}+C$${}=-\mathrm{e}^{3-x}+C$

Accepted Answer

$\displaystyle\int \mathrm e^x\,\mathrm{d}x=\mathrm e^x+C$, and $\displaystyle\int \mathrm e^{ax+b}\,\mathrm{d}x=\dfrac1a \mathrm e^{ax+b}+C$ for $a\ne0$

Integration of Exponential Functions

Integration of Exponential Functions

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