What is the integral of (x+1)ln(2x+4) ?

The integral of (x+1)ln(2x+4) is ln(2x+4)((x^2)/2+x)-(x^2)/4+C

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integral of (x+1)ln(2x+4)

\int (x + 1) ln (2 x + 4) d x

ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4} + C

Solution steps

\int (x + 1) ln (2 x + 4) d x

Apply Integration By Parts

: ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \int \frac{x}{2} d x

= ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \int \frac{x}{2} d x

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4}

Add a constant to the solution

= ln (2 x + 4) (\frac{x ^{2}}{2} + x) - \frac{x ^{2}}{4} + C

\frac{d}{d x} ((\frac{1}{x ^{2}} - \frac{3}{x ^{4}}) (x + 7 x^{3}))

\frac{d y}{d x} = x (9 - y)

\frac{d}{d x} (\frac{1 + 3 x}{1 - 3 x})

x \to \infty lim (9)

- 3 cos (x) + 2 sin (x)

What is the integral of (x+1)ln(2x+4) ?
The integral of (x+1)ln(2x+4) is ln(2x+4)((x^2)/2+x)-(x^2)/4+C