integral of (4x^2+7+2/(x^2+1))

Lösung

\int (4 x^{2} + 7 + \frac{2}{x ^{2} + 1}) d x

\frac{4 x ^{3}}{3} + 7 x + 2 arctan (x) + C

Schritte zur Lösung

\int 4 x^{2} + 7 + \frac{2}{x ^{2} + 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 4 x^{2} d x + \int 7 d x + \int \frac{2}{x ^{2} + 1} d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

\int 7 d x = 7 x

\int \frac{2}{x ^{2} + 1} d x = 2 arctan (x)

= \frac{4 x ^{3}}{3} + 7 x + 2 arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} + 7 x + 2 arctan (x) + C

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

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