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Beliebt Rechnen >

integral of+tln(t+5)

Lösung

\int + t ln (t + 5) d t

Lösung

ln (t + 5) (\frac{1}{2} (t + 5)^{2} - 5 (t + 5)) - \frac{1}{4} (t^{2} - 10 t - 75) + C

Schritte zur Lösung

\int t ln (t + 5) d t

Wende U-Substitution an

= \int (u - 5) ln (u) d u

Wende die partielle Integration an

= ln (u) (\frac{u ^{2}}{2} - 5 u) - \int \frac{1}{2} (u - 10) d u

\int \frac{1}{2} (u - 10) d u = \frac{1}{2} (\frac{u ^{2}}{2} - 10 u)

= ln (u) (\frac{u ^{2}}{2} - 5 u) - \frac{1}{2} (\frac{u ^{2}}{2} - 10 u)

Setze in

u = t + 5

ein

= ln (t + 5) (\frac{( t + 5 ) ^{2}}{2} - 5 (t + 5)) - \frac{1}{2} (\frac{( t + 5 ) ^{2}}{2} - 10 (t + 5))

Vereinfache

ln (t + 5) (\frac{( t + 5 ) ^{2}}{2} - 5 (t + 5)) - \frac{1}{2} (\frac{( t + 5 ) ^{2}}{2} - 10 (t + 5)) : ln (t + 5) (\frac{1}{2} (t + 5)^{2} - 5 (t + 5)) - \frac{1}{4} (t^{2} - 10 t - 75)

= ln (t + 5) (\frac{1}{2} (t + 5)^{2} - 5 (t + 5)) - \frac{1}{4} (t^{2} - 10 t - 75)

Füge eine Konstante zur Lösung hinzu

= ln (t + 5) (\frac{1}{2} (t + 5)^{2} - 5 (t + 5)) - \frac{1}{4} (t^{2} - 10 t - 75) + C

Graph

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