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

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

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integral of (2+ln(x))/x

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

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

Solution steps

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

Apply u-substitution

: \int u d u

= \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= \frac{u ^{2}}{2}

Substitute back

u = 2 + ln (x)

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

Add a constant to the solution

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

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

\int_{- 1}^{5} \frac{8 y}{y ^{2} - 4 y - 12} d y

\int 16 csc (8 x) sec (8 x) d x

x^{2} + 2 x + 1, - 1, 7

y = 8 x, y = x^{2} - 9

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