What is the integral of (ln(x+1))/(sqrt(x+1)) ?

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

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integral of (ln(x+1))/(sqrt(x+1))

\int \frac{ln ( x + 1 )}{x + 1} d x

2 ln (x + 1) x + 1 - 4 x + 1 + C

Solution steps

\int \frac{ln ( x + 1 )}{x + 1} d x

Apply Integration By Parts

: 2 ln (x + 1) x + 1 - \int \frac{2}{x + 1} d x

= 2 ln (x + 1) x + 1 - \int \frac{2}{x + 1} d x

\int \frac{2}{x + 1} d x = 4 x + 1

= 2 ln (x + 1) x + 1 - 4 x + 1

Add a constant to the solution

= 2 ln (x + 1) x + 1 - 4 x + 1 + C

\int_{0}^{1} \frac{x ^{3} + 1}{x + 1} d x

ln (\frac{1}{1 + e ^{- x}})

\frac{d}{d x} (3 x e^{- x} - 2 x)

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

\frac{d}{d x} (2 x + \frac{18}{x} + 1)

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