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

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 1 d x = x

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

Füge eine Konstante zur Lösung hinzu

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

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

\int \frac{30}{x ( ln ( 5 x ) ) ^{2}} d x

\int cos (4 x) cos (x) sin (4 x) sin (2 x) d x

\int sin (2 t) e^{s i n (t)} d t

\int \frac{x}{100 - x ^{2}} d x