What is expand (1+5/(x+1))*(2x+5ln|x+1|) ?

The solution to expand (1+5/(x+1))*(2x+5ln|x+1|) is 1*2x+1*5ln|x+1|+2*5/(x+1)x+5*5/(x+1)ln|x+1|

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expand (1+5/(x+1))*(2x+5ln|x+1|)

expand

(1 + \frac{5}{x + 1}) \cdot (2 x + 5 ln ∣ x + 1 ∣)

1 \cdot 2 x + 1 \cdot 5 ln ∣ x + 1 ∣ + 2 \cdot \frac{5}{x + 1} x + 5 \cdot \frac{5}{x + 1} ln ∣ x + 1 ∣

Solution steps

(1 + \frac{5}{x + 1}) (2 x + 5 ln ∣ x + 1 ∣)

Apply FOIL method:

(a + b) (c + d) = a c + a d + b c + b d

a = 1, b = \frac{5}{x + 1}, c = 2 x, d = 5 ln ∣ x + 1 ∣

= 1 \cdot 2 x + 1 \cdot 5 ln ∣ x + 1 ∣ + \frac{5}{x + 1} \cdot 2 x + \frac{5}{x + 1} \cdot 5 ln ∣ x + 1 ∣

= 1 \cdot 2 x + 1 \cdot 5 ln ∣ x + 1 ∣ + 2 \cdot \frac{5}{x + 1} x + 5 \cdot \frac{5}{x + 1} ln ∣ x + 1 ∣

(1 + 8)^{\frac{1}{2}}

\frac{2 z}{( 1 + z ) ^{2}}

\frac{( x + 1 ) ^{3}}{x ^{\frac{3}{2}}}

4 (sin (4) cos (4) + x cos (2 4^{\circ}))

sin (2 t) U (t - \frac{3 π}{2})

What is expand (1+5/(x+1))*(2x+5ln|x+1|) ?
The solution to expand (1+5/(x+1))*(2x+5ln|x+1|) is 1*2x+1*5ln|x+1|+2*5/(x+1)x+5*5/(x+1)ln|x+1|