Evaluate the integral int(x+4)/(5x+5)dx. Choose 1 answer: (A) (1)/(5)x+(1)/(5)ln |x+1|+C (B) (1)/(5)x+(2)/(5)ln |x+1|+C (C) (1)/(5)x+(3)/(5)ln |x+1|+C (D) (1)/(5)x+(4)/(5)ln |x+1|+C

Simplify the integrand: Simplify the integrand by factoring out the common factor in the denominator. ∫(x+4)/(5x+5)dx = ∫(x+4)/(5(x+1))dxDivide numerator by denominator: Divide each term in the numerator by the denominator. ∫(x+4)/(5(x+1))dx = (1/5)∫(x/(x+1) + 4/(x+1))dxSplit into two integrals: Split the integral into two separate integrals. (1/5)∫(x/(x+1) + 4/(x+1))dx = (1/5)∫(x/(x+1))dx + (1/5)∫(4/(x+1))dxRecognize derivative of natural log: The first integral is the integral of x/(x+1). We can simplify this by recognizing it as a derivative of a natural log. ∫(x/(x+1))dx = ln|x+1| + C

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Evaluate the integral
int(x+4)/(5x+5)dx.
Choose 1 answer:
(A)
(1)/(5)x+(1)/(5)ln |x+1|+C
(B)
(1)/(5)x+(2)/(5)ln |x+1|+C
(C)
(1)/(5)x+(3)/(5)ln |x+1|+C
(D)
(1)/(5)x+(4)/(5)ln |x+1|+C

Evaluate the integral $\int \frac{x+4}{5 x+5} d x$ . $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{1}{5} x+\frac{1}{5} \ln |x+1|+C$ $\newline$ (B) $\frac{1}{5} x+\frac{2}{5} \ln |x+1|+C$ $\newline$ (C) $\frac{1}{5} x+\frac{3}{5} \ln |x+1|+C$ $\newline$ (D) $\frac{1}{5} x+\frac{4}{5} \ln |x+1|+C$

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Find derivatives of using multiple formulae

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Q. Evaluate the integral

\int \frac{x+4}{5 x+5} d x

\newline

Choose

1

answer:

\newline

(A)

\frac{1}{5} x+\frac{1}{5} \ln |x+1|+C

\newline

(B)

\frac{1}{5} x+\frac{2}{5} \ln |x+1|+C

\newline

(C)

\frac{1}{5} x+\frac{3}{5} \ln |x+1|+C

\newline

(D)

\frac{1}{5} x+\frac{4}{5} \ln |x+1|+C

Simplify the integrand: Simplify the integrand by factoring out the common factor in the denominator. \int\frac{x+$4$}{$5$x+$5$}\,dx = \int\frac{x+$4$}{$5$(x+$1$)}\,dx
Divide numerator by denominator: Divide each term in the numerator by the denominator.\(\newline $\int\frac{x+4}{5(x+1)}dx = \frac{1}{5}\int\left(\frac{x}{x+1} + \frac{4}{x+1}\right)dx$
Split into two integrals: Split the integral into two separate integrals. $\newline$ (\frac{$1$}{$5$})\int(\frac{x}{x+$1$} + \frac{$4$}{x+$1$})dx = (\frac{$1$}{$5$})\int(\frac{x}{x+$1$})dx + (\frac{$1$}{$5$})\int(\frac{$4$}{x+$1$})dx
Recognize derivative of natural log: The first integral is the integral of $\frac{x}{x+1}. We can simplify this by recognizing it as a derivative of a natural log. $\newline$ \int\left(\frac{x}{x+\(1$}\right)dx = \ln|x+\(1| + C