integral of x^3+x^2+x+1

Lösung

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

\frac{x ^{4}}{4} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

Schritte zur Lösung

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

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

\int 1 d x = x

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + C

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

\int e^{x} csc (e^{x} + 1) d x

\int 4 sin (\frac{x}{3}) d x

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

\int x^{4} + 8 x d x