integral of θarctan(θ)

Lösung

\int θ arctan (θ) d θ

\frac{1}{2} θ^{2} arctan (θ) - \frac{1}{2} (- arctan (θ) + θ) + C

Schritte zur Lösung

\int θ arctan (θ) d θ

Wende die partielle Integration an

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

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

= \frac{1}{2} θ^{2} arctan (θ) - \frac{1}{2} (- arctan (θ) + θ)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} θ^{2} arctan (θ) - \frac{1}{2} (- arctan (θ) + θ) + C

\int \frac{6 x ^{2} + 8}{2 x ^{3} + 8 x} d x

\int - 2 x e^{3 x} d x

\int \frac{1}{x ^{2} - 2 x - 4} d x

\int \frac{1}{x 25 x ^{2} - 5} d x

\int (5 x^{3} + 7 x - 2) d x