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Beliebt Rechnen >

integral of (ln(t))/(tln(t^2))

Lösung

\int \frac{ln ( t )}{t ln ( t ^{2} )} d t

Lösung

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

Schritte zur Lösung

\int \frac{ln ( t )}{t ln ( t ^{2} )} d t

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

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

Wende U-Substitution an

= \int \frac{1 - 2 e ^{u}}{2} + e^{u} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{1 - 2 e ^{u}}{2} d u + \int e^{u} d u

\int \frac{1 - 2 e ^{u}}{2} d u = \frac{1}{2} u - e^{u}

\int e^{u} d u = e^{u}

= \frac{1}{2} u - e^{u} + e^{u}

Setze in

u = ln (t)

ein

= \frac{1}{2} ln (t) - e^{l n (t)} + e^{l n (t)}

Vereinfache

= \frac{1}{2} ln (t)

Füge eine Konstante zur Lösung hinzu

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

Graph

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