What is the integral of e^3+1/(3-x) ?

The integral of e^3+1/(3-x) is e^3x-ln|3-x|+C

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integral of e^3+1/(3-x)

\int e^{3} + \frac{1}{3 - x} d x

e^{3} x - ln ∣ 3 - x ∣ + C

Solution steps

\int e^{3} + \frac{1}{3 - x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{3} d x + \int \frac{1}{3 - x} d x

\int e^{3} d x = e^{3} x

\int \frac{1}{3 - x} d x = - ln ∣ 3 - x ∣

= e^{3} x - ln ∣ 3 - x ∣

Add a constant to the solution

= e^{3} x - ln ∣ 3 - x ∣ + C

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What is the integral of e^3+1/(3-x) ?
The integral of e^3+1/(3-x) is e^3x-ln|3-x|+C