integral of x^4+3/2 x^2+c

Lösung

\int x^{4} + \frac{3}{2} x^{2} + c d x

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

Schritte zur Lösung

\int x^{4} + \frac{3}{2} x^{2} + c 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^{4} d x + \int \frac{3}{2} x^{2} d x + \int c d x

\int x^{4} d x = \frac{x ^{5}}{5}

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

\int c d x = c x

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

Füge eine Konstante zur Lösung hinzu

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

\int [x (x^{2} - 16)^{2} - \frac{1}{2 x + 5}] d x

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

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