integral of (1-2x)(3+x)

Lösung

\int (1 - 2 x) (3 + x) d x

3 x - \frac{5 x ^{2}}{2} - \frac{2 x ^{3}}{3} + C

Schritte zur Lösung

\int (1 - 2 x) (3 + x) d x

Multipliziere aus

(1 - 2 x) (3 + x) : 3 - 5 x - 2 x^{2}

= \int 3 - 5 x - 2 x^{2} 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 3 d x - \int 5 x d x - \int 2 x^{2} d x

\int 3 d x = 3 x

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

= 3 x - \frac{5 x ^{2}}{2} - \frac{2 x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= 3 x - \frac{5 x ^{2}}{2} - \frac{2 x ^{3}}{3} + C

in t e g r a l sec^{2} (t)

\int \frac{cos ( ln ( x + 1 ) )}{x + 1} d x

\int 5 x^{2} (x^{3} + 1)^{3} d x

\int \frac{x + 7}{x - 1} d x

\int \frac{4 x}{x ^{4} + 4} d x