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Beliebt Rechnen >

integral of (sqrt(t)-3)/(sqrt(t)+1)

Lösung

\int \frac{t - 3}{t + 1} d t

Lösung

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

Schritte zur Lösung

\int \frac{t - 3}{t + 1} d t

\frac{t - 3}{t + 1} = - \frac{4}{t + 1} + 1

= \int - \frac{4}{t + 1} + 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{4}{t + 1} d t + \int 1 d t

\int \frac{4}{t + 1} d t = 8 (t + 1 - ln t + 1)

\int 1 d t = t

= - 8 (t + 1 - ln t + 1) + t

Füge eine Konstante zur Lösung hinzu

= - 8 (t + 1 - ln t + 1) + t + C

Graph

Beliebte Beispiele

integral of x*(ln(x))^2

\int x \cdot (ln (x))^{2} d x

derivative of (x+1/(x^2-y+1))

\frac{d}{d x} (\frac{x + 1}{x ^{2} - y + 1})

y^{''}-6y^'+9=0

y^{^{''}} - 6 y^{^{'}} + 9 = 0

steigung (-5)(0.7)

s l o p e (- 5) (0.7)

integral of 1/(e^v)

\int \frac{1}{e ^{v}} d v