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Beliebt Rechnen >

integral of ln(x+7)

Lösung

\int ln (x + 7) d x

Lösung

x ln (x + 7) + 7 ln (x + 7) - x - 7 + C

Schritte zur Lösung

\int ln (x + 7) d x

Wende U-Substitution an

= \int ln (u) d u

Wende die partielle Integration an

= u ln (u) - \int 1 d u

\int 1 d u = u

= u ln (u) - u

Setze in

u = x + 7

ein

= (x + 7) ln (x + 7) - (x + 7)

Vereinfache

(x + 7) ln (x + 7) - (x + 7) : x ln (x + 7) + 7 ln (x + 7) - x - 7

= x ln (x + 7) + 7 ln (x + 7) - x - 7

Füge eine Konstante zur Lösung hinzu

= x ln (x + 7) + 7 ln (x + 7) - x - 7 + C

Graph

Beliebte Beispiele

integral of 3(ln(x))^2

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

integral of x(x-3)

\int x (x - 3) d x

derivative of (cos(x^3)^2)

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

2xy+x^3=(xdy)/(dx)

2 x y + x^{3} = \frac{x d y}{d x}

integral of (sin(3t+10))/(cos^2(3t+10))

\int \frac{sin ( 3 t + 10 )}{cos ^{2} ( 3 t + 10 )} d t