What is the integral of (1+(1/2)*2/((2*x+3))) ?

The integral of (1+(1/2)*2/((2*x+3))) is x+1/2 ln|2x+3|+C

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integral of (1+(1/2)2/((2x+3)))

\int (1 + (\frac{1}{2}) \cdot \frac{2}{( 2 \cdot x + 3 )}) d x

x + \frac{1}{2} ln ∣ 2 x + 3 ∣ + C

Solution steps

\int 1 + \frac{1}{2} \cdot \frac{2}{2 x + 3} d x

\frac{1}{2} \cdot \frac{2}{2 x + 3} = \frac{1}{2 x + 3}

= \int 1 + \frac{1}{2 x + 3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d x + \int \frac{1}{2 x + 3} d x

\int 1 d x = x

\int \frac{1}{2 x + 3} d x = \frac{1}{2} ln ∣ 2 x + 3 ∣

= x + \frac{1}{2} ln ∣ 2 x + 3 ∣

Add a constant to the solution

= x + \frac{1}{2} ln ∣ 2 x + 3 ∣ + C

\frac{d}{d x} (\frac{sin ( x ^{2} )}{sin ^{2} ( x )})

y = 6 x^{2} e^{- x}

f (x) = 2^{20}

f (x) = 2 - x

\frac{d}{d x} (\frac{( 3 x ^{2} - 5 ) ^{4}}{( 4 x ^{3} + 2 ) ^{5}})

What is the integral of (1+(1/2)*2/((2*x+3))) ?
The integral of (1+(1/2)*2/((2*x+3))) is x+1/2 ln|2x+3|+C