integral of x^2+3x+5

Lösung

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

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

Schritte zur Lösung

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

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

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

\int 5 d x = 5 x

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

Füge eine Konstante zur Lösung hinzu

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

\int \frac{21 x ^{2}}{4 ( x ^{3} + 5 ) ^{\frac{5}{4}}} d x

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