What is the integral of e^{ln(2-x)} ?

The integral of e^{ln(2-x)} is 2x-(x^2)/2+C

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integral of e^{ln(2-x)}

\int e^{l n (2 - x)} d x

2 x - \frac{x ^{2}}{2} + C

Solution steps

\int e^{l n (2 - x)} d x

Apply log rule:

a^{l o g_{a} (b)} = b

= \int 2 - 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 2 d x - \int x d x

\int 2 d x = 2 x

\int x d x = \frac{x ^{2}}{2}

= 2 x - \frac{x ^{2}}{2}

Add a constant to the solution

= 2 x - \frac{x ^{2}}{2} + C

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What is the integral of e^{ln(2-x)} ?
The integral of e^{ln(2-x)} is 2x-(x^2)/2+C