ex, dx=ex+C eax+b, dx= eax+ba+C (a 0) Divide by the coefficient of x in the exponent. If a = 0, the integrand is constant. Check by differentiating. Example Integrate e2x-1 with respect to x. e2x-1,dx = e2x-12+C Integrate e3-x with respect to x. e3-x,dx = e3-x-1+C =-e3-x+C

\(\int e^x\,\mathrm dx=e^x+C\qquad\int e^{ax+b}\,\mathrm dx=\dfrac{e^{ax+b}}a+C\quad(a\ne0)\)

Divide by the coefficient of x in the exponent. If a = 0, the integrand is constant. Check by differentiating.

Integrate \(e^{2x-1}\) with respect to \(x\).

\(\int e^{2x-1}\,\mathrm{d}x\)\({}=\dfrac{e^{2x-1}}2+C\)

Integrate \(e^{3-x}\) with respect to \(x\).

\(\int e^{3-x}\,\mathrm{d}x\)\({}=\dfrac{e^{3-x}}{-1}+C\)\({}=-e^{3-x}+C\)

Integration of Exponential Functions

Integration of Exponential Functions

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