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Beliebt Rechnen >

integral of tln(t+1)

Lösung

\int t ln (t + 1) d t

Lösung

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

Schritte zur Lösung

\int t ln (t + 1) d t

Wende U-Substitution an

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

Wende die partielle Integration an

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

\int \frac{1}{2} (u - 2) d u = \frac{u ^{2}}{4} - u

= ln (u) (\frac{u ^{2}}{2} - u) - (\frac{u ^{2}}{4} - u)

Setze in

u = t + 1

ein

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(2(1+y)x)

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d er i v a t i v e y = 3^{x^{2} + 3 x}

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