integral of (tan(x)+x^{-1}-2x+3)

Lösung

\int (tan (x) + x^{- 1} - 2 x + 3) d x

- ln ∣ cos (x) ∣ + ln ∣ x ∣ - x^{2} + 3 x + C

Schritte zur Lösung

\int tan (x) + x^{- 1} - 2 x + 3 d x

Wende die Summenregel an:

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

= \int tan (x) d x + \int x^{- 1} d x - \int 2 x d x + \int 3 d x

\int tan (x) d x = - ln ∣ cos (x) ∣

\int x^{- 1} d x = ln ∣ x ∣

\int 2 x d x = x^{2}

\int 3 d x = 3 x

= - ln ∣ cos (x) ∣ + ln ∣ x ∣ - x^{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= - ln ∣ cos (x) ∣ + ln ∣ x ∣ - x^{2} + 3 x + C

\int \frac{1}{100 + 2 x} d x

\int (x + x^{2}) d x

\int (3 x + 1)^{2} d x

\int 2 x^{- 1} + 5 d x

\int \frac{16}{25 + 9 x ^{2}} d x