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Beliebt Rechnen >

integral of ln(t+1)

Lösung

\int ln (t + 1) d t

Lösung

t ln (t + 1) + ln (t + 1) - t - 1 + C

Schritte zur Lösung

\int ln (t + 1) d t

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 = t + 1

ein

= (t + 1) ln (t + 1) - (t + 1)

Vereinfache

(t + 1) ln (t + 1) - (t + 1) : t ln (t + 1) + ln (t + 1) - t - 1

= t ln (t + 1) + ln (t + 1) - t - 1

Füge eine Konstante zur Lösung hinzu

= t ln (t + 1) + ln (t + 1) - t - 1 + C

Graph

Beliebte Beispiele

derivative of (sin(x)/(x^5))

\frac{d}{d x} (\frac{sin ( x )}{x ^{5}})

derivative of x^4-2x^2+3

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

tangent y=(x^3-9x)^{10},(3,0)

t an g e n t y = (x^{3} - 9 x)^{10}, (3, 0)

tangent y=3x^3-3x,(-4,0)

t an g e n t y = 3 x^{3} - 3 x, (- 4, 0)

integral from 0 to 3 of (5-5/3 x)^2

\int_{0}^{3} (5 - \frac{5}{3} x)^{2} d x