What is expand (x^2+1)(ln(x^2+1)-1) ?

The solution to expand (x^2+1)(ln(x^2+1)-1) is x^2ln(x^2+1)-x^2+ln(x^2+1)-1

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expand (x^2+1)(ln(x^2+1)-1)

expand

(x^{2} + 1) (ln (x^{2} + 1) - 1)

x^{2} ln (x^{2} + 1) - x^{2} + ln (x^{2} + 1) - 1

Solution steps

(x^{2} + 1) (ln (x^{2} + 1) - 1)

Apply FOIL method:

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

a = x^{2}, b = 1, c = ln (x^{2} + 1), d = - 1

= x^{2} ln (x^{2} + 1) + x^{2} (- 1) + 1 \cdot ln (x^{2} + 1) + 1 \cdot (- 1)

Apply minus-plus rules

+ (- a) = - a

= x^{2} ln (x^{2} + 1) - 1 \cdot x^{2} + 1 \cdot ln (x^{2} + 1) - 1 \cdot 1

Simplify

x^{2} ln (x^{2} + 1) - 1 \cdot x^{2} + 1 \cdot ln (x^{2} + 1) - 1 \cdot 1 : x^{2} ln (x^{2} + 1) - x^{2} + ln (x^{2} + 1) - 1

= x^{2} ln (x^{2} + 1) - x^{2} + ln (x^{2} + 1) - 1

l (e^{2} (t - 3) cos (t - 3))

\frac{( b + x ) ^{4}}{4}

(x + 1)^{5} e^{3 x^{2}}

, (5 a^{2} - 2 b + c^{3}) (3 x - 2 y - 5 z + 2)

What is expand (x^2+1)(ln(x^2+1)-1) ?
The solution to expand (x^2+1)(ln(x^2+1)-1) is x^2ln(x^2+1)-x^2+ln(x^2+1)-1