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

The integral of (1+ln(x)) is xln(x)+C

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integral of (1+ln(x))

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

x ln (x) + C

Solution steps

\int 1 + ln (x) d x

Apply Integration By Parts

: x (1 + ln (x)) - \int 1 d x

= x (1 + ln (x)) - \int 1 d x

\int 1 d x = x

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

Simplify

x (1 + ln (x)) - x : x ln (x)

= x ln (x)

Add a constant to the solution

= x ln (x) + C

2 y^{^{''}} + 7 y^{^{'}} + 3 y = 6, y (0) = 0, y^{^{'}} (0) = 0

f (x) = \frac{2}{x + 7}

\int x cos (3) x^{2} d x

\frac{d}{d x} (5 x^{4} + 3 x^{2} - 9 x + 16)

f (x) = 7 e^{x} + x, (0, 7)