integral of ((t+2))/(tsqrt(t+1))

Lösung

\int \frac{( t + 2 )}{t t + 1} d t

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

Schritte zur Lösung

\int \frac{t + 2}{t t + 1} d t

Multipliziere aus

\frac{t + 2}{t t + 1} : \frac{1}{t + 1} + \frac{2}{t t + 1}

= \int \frac{1}{t + 1} + \frac{2}{t t + 1} d t

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}{t + 1} d t + \int \frac{2}{t t + 1} d t

\int \frac{1}{t + 1} d t = 2 t + 1

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

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

Füge eine Konstante zur Lösung hinzu

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

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