What is the answer to 1/2 (1+1)^2=ln(1)+2/1+2ln(1+1)+C ?

The answer to 1/2 (1+1)^2=ln(1)+2/1+2ln(1+1)+C is C=-2ln(2)

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1/2 (1+1)^2=ln(1)+2/1+2ln(1+1)+C

\frac{1}{2} (1 + 1)^{2} = ln (1) + \frac{2}{1} + 2 ln (1 + 1) + C

C = - 2 ln (2)

Decimal Notation

C = - 1.38629 \dots

Solution steps

\frac{1}{2} (1 + 1)^{2} = ln (1) + \frac{2}{1} + 2 ln (1 + 1) + C

Switch sides

ln (1) + \frac{2}{1} + 2 ln (1 + 1) + C = \frac{1}{2} (1 + 1)^{2}

Apply rule

\frac{a}{1} = a

\frac{2}{1} = 2

ln (1) + 2 + 2 ln (1 + 1) + C = \frac{1}{2} (1 + 1)^{2}

Add the numbers:

1 + 1 = 2

ln (1) + 2 + 2 ln (2) + C = \frac{1}{2} (1 + 1)^{2}

Add the numbers:

1 + 1 = 2

ln (1) + 2 + 2 ln (2) + C = 2^{2} \cdot \frac{1}{2}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

ln (1) + 2 + 2 ln (2) + C = \frac{1 \cdot 2 ^{2}}{2}

Multiply:

1 \cdot 2^{2} = 2^{2}

ln (1) + 2 + 2 ln (2) + C = \frac{2 ^{2}}{2}

Cancel the common factor:

2

ln (1) + 2 + 2 ln (2) + C = 2

Move

ln (1)

to the right side

2 + 2 ln (2) + C = 2

Move

2

to the right side

2 ln (2) + C = 0

Move

2 ln (2)

to the right side

C = - 2 ln (2)

3 \cdot (\frac{- x + 4}{4}) = \frac{1}{2}

2 x + 5 = - 3 x + 10

\frac{y}{8} = - 3

y = 4 \cdot 3^{0}

0.05 z + 0.2 = 0.15 z - 10.5

What is the answer to 1/2 (1+1)^2=ln(1)+2/1+2ln(1+1)+C ?
The answer to 1/2 (1+1)^2=ln(1)+2/1+2ln(1+1)+C is C=-2ln(2)
Solve for C: 1/2 (1+1)^2=ln(1)+2/1+2ln(1+1)+C
The solution is C=-2ln(2)