integral of (3x^2-5x+3)

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{1}{x ^{2} - 8 x - 9} d x

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

\int \frac{x ^{6}}{( 3 + x ^{7} ) ^{2}} d x

\int \frac{12 x ^{2} + 4 x - 16}{6 x ^{2} - 13 x - 5} d x

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