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Evaluate the integral
int(3x+4)/(x+3)dx.
Choose 1 answer:
(A)
=9x-4ln |x+3|+C
(B)
=3x-5ln |x+3|+C
(C)
=3x+5ln |x+3|+C
(D)
=9x-5ln |x+3|+C

Evaluate the integral $\int \frac{3 x+4}{x+3} d x$ . $\newline$ Choose $1$ answer: $\newline$ (A) $=9 x-4 \ln |x+3|+C$ $\newline$ (B) $=3 x-5 \ln |x+3|+C$ $\newline$ (C) $=3 x+5 \ln |x+3|+C$ $\newline$ (D) $=9 x-5 \ln |x+3|+C$

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Evaluate definite integrals using the chain rule

Full solution

Q. Evaluate the integral

\int \frac{3 x+4}{x+3} d x

.

\newline

Choose

1

answer:

\newline

(A)

=9 x-4 \ln |x+3|+C

\newline

(B)

=3 x-5 \ln |x+3|+C

\newline

(C)

=3 x+5 \ln |x+3|+C

\newline

(D)

=9 x-5 \ln |x+3|+C

Simplify the integrand: First, let's try to simplify the integral by dividing the polynomial. We can rewrite the integrand as $3 + \left(\frac{1}{x+3}\right)$ .
Integrate each term: Now, we integrate each term separately. The integral of $3$ with respect to $x$ is $3x$ , and the integral of $\frac{1}{x+3}$ is $\ln|x+3|$ .
Finalize the integral: So, the integral becomes $3x + \ln|x+3| + C$ , where $C$ is the constant of integration.

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