integral of ((3x^2)/(1+x^2)+tan(2x))

Lösung

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

3 (- arctan (x) + x) - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

Schritte zur Lösung

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

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

\int tan (2 x) d x = - \frac{1}{2} ln ∣ cos (2 x) ∣

= 3 (- arctan (x) + x) - \frac{1}{2} ln ∣ cos (2 x) ∣

Füge eine Konstante zur Lösung hinzu

= 3 (- arctan (x) + x) - \frac{1}{2} ln ∣ cos (2 x) ∣ + C

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

\int \frac{1}{10 x ^{2} + 100 x + 250} d x

\int x e^{4 x^{2} + 3} d x

\int e^{a x} sin (2 x) d x

\int (2 x - 1) d x