Question

Math

Posted 5 months ago

```
Integrate.
$\int\left(-\frac{3}{x}+3 e^{x}\right) d x=?$
Choose 1 answer:
(A) $\ln |-3|+3+C$
(B) $-3 \ln |x|+3 e^{x}+C$
(c) $-3 \ln |x|+3+C$
(D) $\ln |-3|+3 e^{x}+C$
```

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Answer from Sia

Verified answer

Posted 5 months ago

Solution by Steps

step 2

The integral of $-\frac{3}{x}$ is $-3 \ln|x|$

step 3

The integral of $3e^x$ is $3e^x$

step 4

Combining the results from steps 2 and 3, we get the integral of the function: $-3 \ln|x| + 3e^x + C$

B

Key Concept

Integration of simple algebraic and exponential functions

Explanation

The integral of $1/x$ is $\ln|x|$ and the integral of $e^x$ is $e^x$, with appropriate constants multiplied. The constant of integration, $C$, is added at the end.

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