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

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 3 d x = 3 x

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

Füge eine Konstante zur Lösung hinzu

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

\int 4 cos (θ) cos^{5} (sin (θ)) d θ

\int \frac{1}{4 - 7 x} d x

\int \frac{ln ( ln ( ln ( x ) ) )}{x ln ( x )} d x

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

\int \frac{10 x}{( 5 x ^{2} - 2 ) ^{4}} d x