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Beliebt Rechnen >

integral of ln(2x+3)

Lösung

\int ln (2 x + 3) d x

Lösung

x ln (2 x + 3) + \frac{3}{2} ln (2 x + 3) - x - \frac{3}{2} + C

Schritte zur Lösung

\int ln (2 x + 3) d x

Wende U-Substitution an

= \int ln (u) \frac{1}{2} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int ln (u) d u

Wende die partielle Integration an

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

\int 1 d u = u

= \frac{1}{2} (u ln (u) - u)

Setze in

u = 2 x + 3

ein

= \frac{1}{2} ((2 x + 3) ln (2 x + 3) - (2 x + 3))

Vereinfache

\frac{1}{2} ((2 x + 3) ln (2 x + 3) - (2 x + 3)) : x ln (2 x + 3) + \frac{3}{2} ln (2 x + 3) - x - \frac{3}{2}

= x ln (2 x + 3) + \frac{3}{2} ln (2 x + 3) - x - \frac{3}{2}

Füge eine Konstante zur Lösung hinzu

= x ln (2 x + 3) + \frac{3}{2} ln (2 x + 3) - x - \frac{3}{2} + C

Graph

Beliebte Beispiele

integral of (5-x^2)/((x^2+9)(3-x))

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

inverselaplace 2/((s+1)(s+2)^2)

in v erse l a pl a ce \frac{2}{( s + 1 ) ( s + 2 ) ^{2}}

(dy)/(dx)=-(e^xy^2)/(10)

\frac{d y}{d x} = - \frac{e ^{x} y ^{2}}{10}

integral of 3ln^2(x)

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

(dy)/(dt)(t)-2y=3e^t

\frac{d y}{d t} (t) - 2 y = 3 e^{t}