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) $\ln |-3|+3 e^{x}+C$

Question

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) $\ln |-3|+3 e^{x}+C$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To integrate the function, we separate it into two integrals: $\int -\frac{3}{x} dx$ and $\int 3e^x dx$. ‖ ‖ 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.⚹◊What is the general formula for integrating $\left(-\frac{3}{x}+3 e^{x}\right) dx$?⍭ Generate me a similar question◊

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